Tough questions are welcome, but they won't sound like "Well, if you think a nationwide basic income is such a good idea, why don't you do it yourself?" That question is only tough because there is no underlying logic to respond to — it's a lazy talking point intended to impugn the other side's motives rather than address the actual issue at hand.
It appears that I agree with you objection, but the heavy use of the word "you" in your question comes across hostile and personal. If you phrased your question in a more passive tone or otherwise referred to unnamed third parties, I'm sure this conversation would have much less of an edge.
I agree that the objection is unconvincing as phrased.
However, if we all agree that "Someone Should Do Something About X", then why does it necessarily follow that government should decree that "Everyone Must Do The Following Things About X: ..."?
There are some gaps in logic there that (commendable!) fervor about poverty does not cover. It's fair to ask whether poverty can be helped by channeling that fervor towards less coercive and bureaucratic (and possibly more effective) outlets.
