In this question:
Should I keep my mouth shut when my boss is wrong?
The key here is "should". Based on your circumstances, you have to weigh being "obedient" against correctness, and building trust against "time wasting" arguing.
In the complexity of life, your boss needs to get things done effectively. Disagreement consumes time and energy. The hard part for you is to determine if that is a good use of time and energy for the both of you. Right now, it seems like it is not productive.
If your boss doesn't trust you and you can't communicate your correctness to him, you are wasting your time. It may be more important for your boss to perceive you as someone "that does what they're told" vs. someone that is "often argumentative and sometimes right." Your boss clearly doesn't see his own errors, so trying to show him the error of his ways is like painting a picture for a blind person; it's the wrong form of communication.
Over time, as you demonstrate that you are compliant and competent, your boss may begin to rely on your opinion as well. Right now, your competence does not seem to matter (sorry - that is borderline insulting, but that is probably why you feel conflicted over this). This is important to recognize since you probably would not bother to "argue" with someone that you see as incompetent. Well, neither does your boss.
You risk making it worse if not only does your opinion/competence not matter, but you also waste time and energy trying to prove points / arguing over "little" issues. Your boss does not sound like the type to take the time to listen to you, so "being right" will probably not be noticed either.
Your boss probably needs time to mature and/or time to learn to trust you. Or else you may need to move on. Bosses that don't trust their subordinates in a skilled profession are usually pretty toxic over long periods of time. Keep quiet and do a good job for a while, try to learn how to produce what your boss asks for as quickly as possible, wait to see if your opinion is heard (or, ideally, asked for) and then take action as needed.