Logical inconsistency
Logical inconsistency is when you say two things that can't both be true at once, or you argue for one thing and then the opposite. Your position contradicts itself. That doesn't mean either claim is false by itself, but together they can't stand. The fallacy is to hold or assert inconsistent views. The remedy is to drop or revise one of the claims so they're consistent.
Examples
We should never get involved in other countries. We should also send in troops when human rights are abused.
I never lie. I just didn't tell you the full truth.
We must cut the deficit. We must also increase spending on everything we care about.
Everyone should follow the rules. But I'm an exception because my case is special.
Free speech is absolute. But we should ban that kind of speech.