Zenyatta is at least an actual healer. Symmetra's kit does almost nothing to actually support anyone - even her barrier is, well, a barrier. You could make a better argument for her being a tank because she blocks attacks with it.
Fact is that she initially seemed like a disc priest sort of "support" with the shielding and that was a bit awkward. When that got removed she still just sorta sat in the support category for whatever reason, and now Blizzard has seemed a bit lost on what to do with her and has thrown an alternate ultimate on her to try to shoehorn her back into that role.