Other than Kendra and Carter, who are needed on the team for self-evident reasons, the only indication we're given for how Rip chose the rest of the Legends is in his confession near the end of the first episode:
Rip: I chose you all because, a hundred years from now, your lives have minimal effect on the recorded timeline. I needed your help without disturbing the history of 2166.
Legends of Tomorrow Season 1 Episode 1: "Pilot, Part 1"
This is clearly an oversimplification, since each member of the team does bring skills to the table. However, the reason for choosing - for example - Ray Palmer over Oliver Queen would seem to be this one.
So, it would seem that Barry and Oliver are just more important to the timeline than the others are. Although we don't know much about Arrowverse history post-2016, there is some limited evidence for this:
- I'm guessing at the end of the current season of Arrow, but Oliver appears instrumental in preventing Hive from doing some Bad Things in Star City
- Oliver is also instrumental in Grant Wilson's (Deathstroke's son's) rise and fall, as seen in the Legends of Tomorrow episode "Star City 2046"1
- Barry is an extremely public figure in Eobard Thawne's future, though the exact impact of his actions is unknown
1 This may not be a good example, since it's unclear to what extent the events of that episode were caused by Ray and Sara being removed from the timeline. In the episode, Oliver suggests that their absence was very relevant to the Bad Future, but that would seem to contradict Rip's statement that they were unimportant. YMMV.