Sophists, relativism

I'm not extra knowledgeable in the history of philosophy. Still, now we're learning philosophy in the school during Social sciences lessons and it sparked my interest.
Sophists are portrayed as "the bad ones", though we actually know rather little about them. They accepted payments for their teaching. Now, how should they make their living? This way they could mostly retain their independence (contrary to the possibility they'd have a single patron.
They taught how to rig logic to one's advantage. Now, we don't know if it was all of them doing this or just a part of them. We also don't know, if they taught just these rigs or also "normal" logic and rhetoric (which seems likely). But it doesn't matter. First, if they believed in pragmatic and subjective truth, it seems no problem to me if they taught how to deliver one's truth to others by every means possible. Also, if one doesn't like this, I may argue that by being taught how to rig logic, you also become more able in seeing through the rigged logic.
After all, sophists are also portrayed as a homogeneous group by many (Plato...) - easier to criticize a nameless crowd than a single thinker, huh?
And about the relativism - I was surprised that even Mr. Klein (our Social sciences teacher) claimed relativism led to the decay of society. Plainly said, it's "bad". Sophists' relativism should have stem from the huge variety in opinions held by contemporary philosophers - similar to the situation of nowadays, isn't it?
Perhaps, relativism may be unpleasant to people who hold strong opinions about something. One is polishing their own opinions for all the life, confronting it with their plentiful experience - it's then simple to say others just must be wrong, rather than that their opinion is as valid as mine. Yet it seems to me, even if we dismiss totally implausible opinions (still how may I absolutely dismiss an idea of anyone, even though the person came to it by means I deem wrong, implausible, stupid, naive...?), there is a lot of opinions, differing a lot, but rejectable often only on base of one's preferences and values (I see it just too often - only talking with my relatives, friends...).
If relativism leads to the decay of the society? If "decay of the society" means little (or, not sufficient) approval of one's own opinions among the rest of people, then probably yes...
The trouble in believing in one objective truth is that it's usually your opinion, that is the objective one...