Why are thighs important?
Genesis 24:2 NIV
One day Abraham said to his oldest servant, the man in charge of his household, “Take an oath by putting your hand under my thigh.
Genesis 47:29 NIV
As the time of his death drew near, Jacob called for his son Joseph and said to him, “Please do me this favor. Put your hand under my thigh and swear that you will treat me with unfailing love by honoring this last request: Do not bury me in Egypt.
Leviticus 7:33 NIV
The right thigh must always be given to the priest who offers the blood and the fat of the peace offering.

The Hebrew term often translated "thigh" is ירך (yārēḵ; יָרֵךְ), which HALOT notes can refer to (my numbering; HALOT has only 2 entries and groups a number of meanings under #1 of there entry):
1.    The upper thigh (upper leg); e.g., Exo 28:42 (distinct from the waist here, referring to the bottom extent of priest's trousers), Jer 31:19 (Jeremiah surely struck a part of his leg), probably Song 7:1 (the two thighs of the woman described)
2.    The side of the hip (hip joint connecting the thigh); e.g., Gen 32:21-32 (Jacob's muscle shrank there), Exo 32:27 (a place for the sword to hang)
3.    The area of the genitals
•    as the place from which male procreation occurs; e.g., Gen 46:26 (KJV: loins; NKJV: body; others descendents), Exo 1:5 (KJV & NASB: loins; others descendents); part of the whole phrase "came out of the loins" is what is sometimes being translated as some phrase with descendents, but this term is there in the Hebrew text.
•    as the place of female procreation (Num 5:21ff)
4.    As a metaphorical extension of #2 to mean the "side" of something (or my conjecture is that it is more related to the "support" of something, which often is at a "side," except see the last example here); e.g., Lev 1:11 (side of the altar), Exo 40:22 (side of the tabernacle), Exo 25:31 (shaft of the lampstand)
NOTE: The Leviticus 7:33 reference is a totally different Hebrew word שוק (šq; שׁוֹק), and so is distinct from the term yārēḵ.
Two Primary Options
Regarding the oath formula, there are two options to the use of the term yārēḵ:
1.    a literal reference to one of the most powerful muscles of the human body (figurative of strength)
2.    a literal or figurative (euphemistic) reference to the genital area (but ultimately figurative of its procreative power).
For the oath passages Gen 24:2, 9 and 47:29, some insist the context makes it clear it is a reference to the genitals. An example is James M. Freeman and Harold J. Chadwick, Manners & Customs of the Bible (North Brunswick, NJ: Bridge-Logos Publishers, 1998), page 34 (bolding shows the "insistence" of their view):
The word thigh—Hebrew, yarek—is a euphemism; that is, a mild or indirect word that is substituted for one that is considered too harsh, blunt, or offensive. Without question, the servant’s hand was placed beneath Abraham’s procreative organs (these words are also euphemisms). Whether the placement of the hand had to do with the act of circumcision instituted by God, and thus gave a covenant solemnity to the oath, is not known. It has been said by some that it had reference to the long-range effects that the servant’s mission would have upon Abraham’s descendants, or that it symbolized that even his yet unborn children would avenge any violation of the act. But neither of these explanations seem to fit Israel’s request to his son Joseph to take his body out of Egypt and bury it where his fathers are buried, when the same manner of swearing an oath was used (see Genesis 47:29).
Another quote, this from John J. Pilch, A Cultural Handbook to the Bible (Grand Rapids, MI: William B. Eerdmans Publishing Company, 2012), page 280:
Other common words like thigh, hand, and finger also symbolize reproductive parts of the anatomy where the context makes this clear. When Abraham commands his servant: “Put your hand under my thigh, and swear to me by the LORD that you will do my bidding,” the servant must swear while his hand touches Abraham’s organ (see Gen. 24:2, 9). The deed is clear, but its significance is less clear. One interpretation is that the person is swearing by touching a sacred spot, namely, the location of the “covenant of circumcision.” Another interpretation is that if the person does not fulfill his oath, he can expect punishment in this vital region of his body. He might not produce further progeny.
However, despite this common view, insistence on the oath passages referring to the genitals cannot be fully maintained given that clearly the term is used not in reference to the "procreative organs" in other passages. So the term is not exclusively euphemistically used, and the question remains if that is really what is intended in these two passages.
Even if the procreative power is the emphasis of the oath (and there is not a guarantee such is the case), it may be that "thigh" or "loins" takes on that association itself figuratively. That is, the oath itself may not have been with the hand "placed beneath ... procreative organs," but only literally "under the thigh [of the leg]" with that association still being a reference to the procreative power of the loins in general.
So procreative power may be the emphasis. Yet the emphasis may be to an individual's strength, for the thigh/hip area is critical to overall full body strength. Without both thighs/hips being healthy, a person cannot walk well (so Jacob, Gen 32:31), neither do much in the way of lifting, turning, etc. This idea fits better as well with the figurative use of the term in definition #4 above, where the sides (or shaft) are the strength of support to the structures.
Contextual Analysis
In Gen 24:2 and 9, the context of the passage refers to the descendants. Abraham is seeking a wife for Isaac in chapter 24, and the purity of her is important (v.3) with respect to the promise of descendants given to Abraham (v.7). This yields some plausibility to the procreative power being the focus of the oath.
But in Gen 47:29, Jacob (Israel) is making Joseph swear an oath to not bury his body in Egypt, but to take it back to be with his fathers (v.30). This has no relation to descendants, but rather to ancestry.
Really, what both have in common is a focus on the promise of God with respect to the land and its people. Jacob wants to be buried in the promised land, where Abraham and Isaac are buried. Abraham wants a wife for Isaac brought to the promised land (Gen 24:4-7), without Isaac leaving that land (v.6, 8). It is there that Abraham's descendants are promised a place (v.7). So the common focus is on the strength of God to fulfill what He has promised (explicit in Abraham's request, implicit in Jacob's desire to be buried there).
Recall that Abraham specifically has his servant "swear by the LORD, the God of heaven and the God of the earth" (Gen 24:3, NKJV) while placing hand under thigh. Whether this was so for Joseph's oath to Jacob is less clear, though there was certainly some distinction between Joseph's statement "I will do as you have said" (Gen 47:30) and Jacob's follow-up "Swear to me," of which Joseph then "swore to him" (v.31). It may well be that the oath swearing was related to YHWH's name, though that is still not explicit.
While I also cannot "insist," I find more support for the idea of thigh in the oath passages referring to the strength of the individuals, but not their own strength (of which Jacob's was taken), but rather the strength of the One they both trusted in to fulfill His promises. By having another swear with "hand under the thigh," the actions (represented by the hand) of those individuals are placed under oath to trust in the strength of YHWH (represented by the thigh of the believer) to play a part in working to fulfill YHWH's promises.
However, whether or not the procreative idea is to be favored instead of the strength idea, it seems most likely that the swearing itself would have been literally "under the upper leg," not "under the genitals," and the procreative idea expressed through the figurative association of the loins to procreation if that is to be favored, while the figurative association is more direct to the strength of the muscle if that is to be favored.
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answered Nov 9 '16 at 18:33

The concept/s behind this focus on the male organ becomes moot when it is set amid the land they had come to occupy, Canaan, which was the epitome of matriarchy from before history. When fatherhood, the ultimate dubious concept, is confronted with its irrelevance it is emasculating. The crucial aspect is the circumcision which instantly sets them as aliens, self selected and thereby encumbered. This did not inhibit Judah with Tamar (Gen38:10-30) but, hey double standards, wotcha gonna do?
As their monotheism was incompatible with worship of the Great Mother so their flocks from the high country, sheep & goats, were supremely deleterious to the long settled land of agriculture. (They adopted bovis & bos post invasion, long afterwards.) Apart from the botanical damage & grazing (both short & long term, ie sapling regrowth) the effect trampling hooves, small & sharp, on irrigation channels was dire & total. In a flat land without rain, crops can only be grown with great care of water resources. The "torrent valleys" away SE in Moab were created by denuding the hillsides.