It seems that at the time that 1 Timothy was written, "certain people" had become much too interested in genealogies:
1 Timothy 1:3-4
3 I repeat the request I made of you when I was on my way to Macedonia, that you stay in Ephesus to instruct certain people not to teach false doctrines 4 or to concern themselves with myths and endless genealogies, which promote speculations rather than the plan of God that is to be received by faith. 5 The aim of this instruction is love from a pure heart, a good conscience, and a sincere faith. 6 Some people have deviated from these and turned to meaningless talk, 7 wanting to be teachers of the law, but without understanding either what they are saying or what they assert with such assurance.
Other passages in the Bible, such as Genesis 10, Genesis 5, and Matthew 1, list various geneologies. These hardly seem to qualify as "endless", unless one has a very short attention span. So what exactly is 1 Timothy talking about? I would guess, especially based on the context, that "certain people" were more or less fabricating geneologies about biblical figures, but on what basis? And is this a prohibition against being interested in any genealogies, or is it referring to a specific sort of interest? Most importantly, is it a prohibition against reading and being interested in the geneological parts of the Bible itself, provided that one remains interested in only what is said therin?