Anything can be a support but you have to be playing support. I checked your match, your adc was 1/6 while you were 5/3 (this was the most recent one)
Now I don't know if you were trying to get them kills and the adc sucked and you guys got ganked a lot. I'm not saying you weren't trying, I'm just saying in general to everyone, if you want to take a champ who isn't a support in the support role, please actually support, because I have so many people pick midlaners, build damage, and take all my kills so I fall behind and become unrelevant. This is in no way to attack you or anything, I'm a support main and I've been one for almost 2 years so I'm just trying to help.
I'm looking at the most recent match by the way, idk if it is that one so I checked all of them that you have as syndra in normals, and you didn't build sight stone at all in any of them. You built a midlane build, and that is why they got mad at you.
Warding is a part of the support role, and while EVERYONE should be warding, a support should be warding the most and destroying enemy wards. You must build a support item as these are your main source of gold income besides assists and kills. You have around 100 cs in each game, and if you got that cs in lane do not continue, because cs is how your adc is getting gold. Taking their cs when they are in lane puts them behind the other adc. I believe around 15 cs = a kill's worth of gold, so if your adc is 15 cs behind the enemy adc they are behind a kill.
Always get
, it gives you 3 wards that last longer than yellow wards and also some health. After getting Sightstone, I usually get
and eventually upgrade to
. This allows you to destroy enemy wards. If you do not get rid of enemy wards, your jungle will not be able to gank because they will always see him coming, you'll be spotted taking important objectives like drag and baron, and if you're going in to take out a straggler farming in lane they will see you if they warded. It is also good for making sure they don't have vision in your own jungle, if they see your jungler they might invade to kill him. Red trinket and Sightstone are very important and every support should have both imo.
ALWAYS build a support item, and for syndra I'd suggest
as it gives you a slow, damage, cdr, and gold upon hitting the enemy which is what you'll be wanting to do since syndra has a lot of poke. If you think you're going to have a hard time in lane and not be able to poke safely, build
because you'll get gold for every nearby minion killed, cdr, and it gives you a speed up.
Once you have your support item and sightstone, then you can start building damage. They most likely got mad because you didn't have a support item, a sightstone, and built a straight midlane build, however if they were not contributing to wards they are still at fault.
I also see you don't have a keystone, and personally for syndra I like deathfire. It adds a nice little extra damage to your poke and I've actually gotten kills with it (the best was I ulted someone as Cait and it didn't kill them right away, so I was like "awwww" but then the deathfire finished them off XD)
So basically, to sum that all up in a tl;dr
- Always buy a sightstone and upgrade it later in game
- Make sure you get a red trinket after sightstone and then upgrade it at lvl 9
- Build a support item, I personally suggest
for syndra but if you cannot safely poke I'd get 
- Always use all your charges on sightstone before backing and during the laning phase make sure gank points are clear of wards so your jg can come in undetected
And I'm just going off of the games I see on op.gg . The most recent game was from a day ago so idk when you played this game you are speaking of, but I'm just going off of that so sorry if you did all of this and I'm just not seeing it e.e
Also I main Nami and Sona support with the occasional Soraka