Yes, there is a rhyme and reason, but because that requires actually delving into linguistics studying (plus etymology for all those edge cases that got carried over from Latin and other languages), most people don't get too deep into it apart from shallow rules (eg: if word starts/ends in X then it's male/female).

Not even natives of gendered languages usually bother learning the nitty gritty rules, they just pick it up as they go, that's how all of us learn our languages.

On a practical level, it's also much easier to teach a 6 year old in elementary that something is male/female just because, and to remember that, than to go into each and every individual case (morphology, syntax, semantics, etc.), which themselves typically have edge cases due to history and whatnot. Especially because that child will naturally pick it up as they absorb the language around them so it really doesn't matter much.

And then there's just those cases where we actually don't know because the etymology got lost. Yeah, that's fun.

In school I was never taught why something is male/female yet I can always distinguish them naturally in my. day to day because that's how I've always lived. That's just one of the amazing things of human language.

If you ask a native of a gendered language why they think X word should be male instead of female they'll probably just tell you it sounds wrong otherwise, and that's literally the end of it for most of us. We don't think about it, we just intuitively know it sounds right or wrong. I'm sure that's frustrating to hear for a foreigner trying to learn, but you can't teach what you don't know. In the end, other than very broad rules, the best way typically is to just start memorizing it one by one.

Also, "ends in A" is definitely rhyme or reason in Portuguese, that's actually a rule. Although to be more specific it's a tonic A, but even that has an exception if it's a nasal Ã, but I didn't want to get into phonology too, I just wanted to give a simple example.