Equating conscription with slavery conveys strictly less useful information.

There are many social constructs that forcibly remove rights from someone while retaining others.

The set of rights a conscript loses is radically different from the set of rights a slave loses.

As a citizen of the US who is not of cosncription age, am I "slave" because the government has removed my right to own nuclear weapons or kill bald eagles? No, obviously not. While conscripts are forced to do some things, they maintain many rights and are treated as people, not property, under law.

But conscription is neither slavery nor forced labor (like taxes aren't theft), because parties to ECHR agreed to give themselves exemption on that.

well... it is, but mostly for economic reasons. Contract army is the privilege of the very richest countries, and in most favorable conditions, too. To me, the idea to be obligated to go and die in some random place like Vietnam on the other side of the planet is obscene. But no society seems to escape this to a certain extent. Except... a few ultra-privileged ones, in peaceful times.

Think of it as less of a euphemism, and more of a specific type of slavery.