> In the US there's no explicit right to vote.

Yes, there is.

There is no explicit general prohibition on laws impairing that specific right the way there is some other rights, but the existence of the right is explicit, among other places in Amendment XV, Sec. 1: “The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of race, color, or previous condition of servitude.” This explicitly states that the right exists, and then goes on to prohibit denying or abridging it on an enumerated set of bases. (There's two other voting rights amendments following the same pattern.)

This implies that the right can be denied for other reasons, which would mean that it's not an inherent right of citizens. And, indeed, courts do not consider e.g. restrictions on voting for citizens with criminal records to be unconstitutional.

And it's not like it's a new invention. I mean, women couldn't vote back when 15A was passed, and they still couldn't vote after. It wasn't a surprise, either - many suffragists opposed 15A even before it was ratified for this exact reason, because its wording made it clear that it wasn't covering sex.

To add to dragonwriter's post, there is also the 17th amendment:

"The Senate of the United States shall be composed of two Senators from each State, elected by the people thereof, for six years; and each Senator shall have one vote. The electors in each State shall have the qualifications requisite for electors of the most numerous branch of the State legislatures."

It's exceptionally clear that it's an explicit right to vote for the election of senators.

Why couldn't women vote for Senators then?