Let's take the following propositions :

1 - "If Bill Gates is poor then Bill Gates is rich".
2 - "If Bill Gates is poor then the moon is made of cheese".

Both propositions are inevitably true under the usual interpretation (our current world,) and I completely understand the reason.

The reason is that we don't have a situation where the antecedent is true and the consequent is false, so the proposition is true (even if it is vacuously true).

But there is something which is intriguing me.

Even though, some say that both 1) and 2) are a bit weird (the issue some people have with vacuous truth) , why between 1) and 2) people usually find 1) a bit more weird than 2) ?
In another words, why when p is false, the truth of the proposition "p -> q" sounds a bit more weird if q is ~p compared to other situations where q is arbitrary ?

One possible conjecture (which is probably wrong) is that people find that "p and ~p" ought to be false and perhaps in the natural language the implication resembles a bit conjunction. But I don't know if it does.

Anyways, does anyone have an idea about the issue?

P.S : I wanna emphasize here that my problem is not with relevance or vacuous truth, but rather the difference between 1) and 2) ( both of which suffer the problem of relevance ).
Thanks