They (and their families) haven't been paying taxes into the community their entire working lives like the natives have. The argument is that the people who have been contributing to the society more and for longer should get to see some benefits from the system before someone who has contributed literally nothing to your community shows up. That's why out of state students pay way more for tuition than in-state students at public universities.
Even if you have some wacky reason for disagreeing with this logic, then take the taxes out of it. What's wrong with caring about your fellow citizens who's vote might affect your more than someone that's possibly displacing them?
Um, I guess thank you for defining my reasoning as wacky. Turns out, I agree with your logic, but want to point out that it doesn't lead to the conclusion that you support.
1. Do you like the fact that out-of-state/country students pay more for tuition (thus subsidizing the education of the good native people)?
2. If so, do you like the fact that H1B pay taxes (thus subsidizing Social Security for the good native people)? The H1B is term-limited to 6 years, and people need to leave the country if they no longer work (or pay taxes). So the do NOT benefit indefinitely at the expense of the community who have been long-term tax payers. With respect to tax, the H1B is totally a pay-to-pay (a little bit pay-extra-to-play, even) visa.
[Edit: We already established that H1B holders can NOT vote. So they cannot affect your community of long-term tax-paying natives in that manner].
Even if you have some wacky reason for disagreeing with this logic, then take the taxes out of it. What's wrong with caring about your fellow citizens who's vote might affect your more than someone that's possibly displacing them?