The United States is not your "home". YOU, or any other individual citizen...is not the "sole" owner. Those who do not pay taxes into the system (which, in and of itself, is a dishonest misnomer) are not "guests", they are co-owners whether or not you like it. The fact that you see that analogy as legitimate inherently indicates a flaw in your thinking.
I'd perhaps be more understanding if people were somehow claiming that this stance should be taken across the board. That not only that those on welfare shouldn't be able to vote, but that the WEIGHT of ones vote should somehow inherently be tied to how much taxes they pay. Indeed, the guy paying millions of dollars into taxes is being forced to "provide" things like roads, schools, police, national protection, etc for YOU and others who are likely not providing anywhere near the same level as him....should we allow his vote to count 100 times yours for electoral purposes while we're simultaneously disallowing those on welfare from voting?
Will those on welfare often try to vote for what's going to be best for their life and their situation, not what's necessarily "best for the country"? Absolutely. Guess wha. Middle class or upper class people, paying a good bit of taxes, are going to be doing the same thing. That's what voting is. And that's a right as a CITIZEN people should have...and not one that should be taken away simply because you think that the way THEY benefit of the government is inherently bad, but the way YOU benefit from the government is perfectly okay.