As others have mentioned, the problem with branches in SVN isn't the branching, it's the merging. IIRC, this was because SVN didn't track merges, so if for instance you have a "stable fixes for release X" branch which is repeatedly merged into the trunk, you'd soon encounter wonky behavior.
Subversion absolutely tracks merges, but you don't really need that just to keep a stable branch regularly updated. That's a very normal and expected use of a branch and should not give you "wonky behavior" in neither git nor svn. Thousands of projects do it every day. Any encountered problems are likely not inherent to your version control system.
It definitely didn't use to track merges. That got added after most people jumped ship to git. Before that, you had to specify the common ancestor commit of the things you were merging, which you usually didnt know and had to dig around in slow logs to find out.
It has tracked merges longer than github has existed, just to keep things in perspective. But, again, it's not required just to keep stable branches around since commit numbering is linear in svn. It's very convenient for anything less trivial than that though.
