That's not a common connotation; I've never once seen anyone use those phrases to mean that. "two or three" does not typically have any connotation of either being more likely.

Might be something specific to where you are?

What I described is how this construct is used in every place I lived.

Have you ever lived in the UK? Because I've never thought of "two or three" as meaning that two is more likely than three.

Are you sure that other people actually mean this when they say it, or are you just adding the extra connotation in your head?

Also I'm not sure I've ever heard anyone say "three or two". That sounds weird, like saying "fork and knife".

Lest anyone draw the conclusion that this is a US thing, it certainly is not. I've lived in many places throughout the US and have never heard anyone say "three or two". Nor does "two or three" carry the connotation that two is likelier. A closer fit to that would be "a couple", which formally means two, but sometimes means "a small number".

Not in the UK, no. But I did live in Canada, the US and across Europe.

Not that it's commonly used and not with 3 and 2 specifically, but when used and the pair is inverted, it's meant to convey that the former is more likely. That's just like ... common sense, really.