Luke didn't record Lord teaching him. Instead, he only records audaciously that the Lord was pleading him not to persecute Him.
Act 9:13 And
Ananias answered, `Lord, I have heard from many about this man, how many evils he did to Thy saints in Jerusalem,
Act 9:14 and here he hath authority from the chief priests, to bind all those calling on Thy name.'
Act 9:15 And the Lord said unto him,
`Be going on, because a choice vessel to Me is this one, to bear My name before nations and kings--the sons also of Israel;
Act 9:16 for I will shew him how many things it behoveth him for My name to suffer.'
So now you would call Ananias a liar as well. Major conspiracy going on it seems. Paul, Luke, Peter, Ananias, etc.
Does he think that not seeking support is a kind of injustice? What was he talking here?
Para...If taking nothing from you is proof that I am not for you, then forgive me for this injustice to you.
In other words, it does not make any sense to accuse him of being self-serving (injustice to them) when he hadn't taken anything from them. Therefore,
they must think that not taking anything from them was an injustice to them. He was pointing out how nonsensical the false prophets accusations were against him and they were not thinking rationally to believe it.
This is the worst thinking of Paul who had no experience as a parent. It is children who should support and honor parents. Jesus condemns those who avoid that.
The Apostle John also calls the people, 'my little children'. This is how Paul thinks of them, as though they are children that he should be care for. Not giving them an inheritance in earthly goods but spiritual truths.
Jesus taught against Korbin. Children are cared for by the parents as they are growing up. Parents don't ask their children to provide the parent with the necessities of life. When the parent cannot take care of themselves it is the child's turn to care for them.
When the parent can longer run the family business, farm, etc. they give to over to the child, as an inheritance. Anything that they have stored up goes to the child. Then the child sees that the parent is cared for.
Korbin said that the child could dedicate what they had to the temple, while still having control over it and using it any way that they chose. But when it came to using it to take care of their parents they could claim they couldn't because it had been dedicated to the temple. Out and out lying in order to hang on to their goods and the greedy Pharisees had made this rule.
This is what Ananias and Sephira had done when they lied about giving everything from the sale of their property. Peter tells them that they didn't have to give it, it was still theirs to do with as they chose, but they lied about it.
You are overlooking his strategy of pleasing everybody to push his agenda unsupported in any another place in the Bible. For example, for the gibberish talk that imitated badly the happening on Pentecost in Corinth, he claimed that he also spoke gibberish!
He never claimed any such thing. He said he prayed with his understanding and in languages he, himself, did not understand. That doesn't mean they were gibberish. Read what he said to them. In public, do not speak a language that you or someone else cannot interpret, it will not edify anyone there except yourself.