Lots of people like to declare what motivates people to disagree with us. Maybe instead of finding the most sinister reasons, be a little more evidence based. Because they want to split the vote isn’t a very well supported evidence based claim. If it’s all that difficult for you to figure out why Libertarians vote for Libertarians, and you won’t bother to consider all the ways you might be different as a primary motivation, maybe you should just ask Libertarians.
Here’s a clue. The card carrying, Ayn Rand worshipping real ass Big “L” Libertarians don’t agree with a lot of the Republican platform. They don’t agree on abortion, gays, drug war, military spending, foreign entanglements, patriot act, citizens united, basically most social issues, and the list could go on and on. Just because they share some common positions, they are not right wing per se, though some are. Many are left wing.
If you really have to guess why, rather than just assuming some nefarious reason, like, oh, they must just want to split the vote, maybe you could recall all the arguments with INGO’s Mr Jarrell. That dude was the epitome of the reason that many Libertarians won’t vote for Republicans. It’s because, though they also distrust government, support the 2a, etcetera, they are not Republicans.
Do you think the democratic socialists in the D party said the same thing about the D establishment? No of course they didn't. They have worked within the D party to pull it further to the left and look where they are now.