I've been a moderator on several pretty active forums, and I can offer a few reasons:
It shifts focus away from new posts.
This is probably the number one reason. Most active users sort posts by date so that the new posts go to the top. This allows users to focus on questions and discussions as they come in. Posting to an old thread "bumps" the old thread to the top, which shifts our focus away from new posts to old posts. That might not be a big deal, except:
Most old posts have been abandoned.
Most threads are from new users, mostly with a specific question. That question is then either answered, or it's not answered and some time goes by and the user abandons the question.
Many "bumping" posts are answers to questions that have either already been answered or have been abandoned. If the OP hasn't visited the forum in a year, why spend time answering it? Why make other people spend time reading your post?
It makes old threads harder to read.
Let's say a thread starts, then is abandoned for a year, then you make a post, some discussion ensues, and then another year goes by. Now I as a reader stumble across the thread. The actual answer that was originally in the thread is now somewhere in the middle of the discussion instead of at the bottom. I now have to figure out when each post was made, when the answer was posted, what happened after that, etc. It would be much better for me if this had been split into two separate threads.
This can trigger discussions on abandoned threads.
Another thing I see very often is that one "bumping" post will cause the thread to rise to the top, which will cause other users to jump in, not realizing that the OP is long gone, and continue a discussion that has long since been abandoned. This creates a bit of a snowball effect as more active users spend time in that thread instead of on actual new conversations.
This might not be an issue if the discussion is actually interesting, but most of the time it's not.
Most bumping posts are low quality.
Maybe your bumping post really does add something interesting, and maybe it does spark an interesting conversation. But 95% of the time it's a drive-by hit from a Google search, either offering a solution to an old problem (see above) or saying "thanks me too!" (notice that Stack Overflow disallows posts like this) or saying "I have the same problem, did you ever fix this?"
Those types of posts might be useful to you as a poster, but they aren't useful to the forum as a whole, and they especially aren't useful to power users who are policing the forum.
It's hard to decide whether you're an exception to the rule.
Considering that 95% of bumping posts are low quality, it can be "hard" or time-consuming to take the time to read your post and the thread you've bumped to decide whether your post belongs there or not, then to reply to you asking you to start your own thread, or to lock the thread, or to take whatever action is now required of us.
Most necromancing posts belong in their own thread.
If you think that your post would be useful, maybe because you're having a similar problem and the posted solutions didn't work for you, then your post belongs in a new thread. Instead of continuing the old discussion, start a new discussion and link to the old one.
This avoids all of the problems above, but allows you to ask follow-up questions or start a new discussion.
Our time is free, but it's not worthless.
Keep in mind that you aren't just talking to the OP. You're talking to everybody on the forum, particularly "power users" who sort by date. They're all going to read your post. They're probably going to re-read the entire thread.
That might not seem like a lot of work, but keep in mind that many of these users are also moderating the forum, deleting spam (so much spam), banning rude users, answering questions, etc. We do this for free, in our spare time. You might think "what's the big deal if I make you spend a few minutes re-reading a thread", but moderating a forum is a zero-sum game. I only have a certain amount of time to do all this stuff. The more time you make me spend on old threads is less time I can spend banning spammers. So the more time you take away from us by bumping old threads, the less time we have to actually do our "jobs" on the forum.
Especially because the fix is easy. Just post a new thread with a link to the old one.
I know that some (or maybe all) of these issues can be addressed with different forum software. I really like Discourse, although it suffers from some of the same issues. And I know there are exceptions to all of the above. But if you're asking why forums (specifically the power users on those forums) frown on bumping old threads, these are some of the reasons why.