A low kill count is not a bad thing on supports. Supports champions are distinguished by their ability to contribute to the team with very little gold. They lane with a high damage champion, typically an ADC, to help them get enough gold to carry the middle and late game. This is why supports tend to avoid killing lane minions when an ally is near enough to take them instead, and it is why they try to avoid taking kills if a carry is near enough to deal the finishing blow. Barring solo kills, my ideal KDA on a support is 0/0/X, where X is any large number, preferably at least half as large as my total team kill count. I get enough gold from assists to keep up with the team, while the damage dealers on my team get the kill gold, allowing them to snowball ahead of our opponents. Of course, it is important to keep from dying whenever possible, since your deaths will give enemies gold. The exception is sacrificing yourself to prevent the death of a teammate, if you believe your teammate's survival will be more beneficial for your team than your own. That said, don't throw yourself into harm's way unless you are certain your fed Draven will escape; it's not usually worth the risk of giving up two kills instead of one.
It is fine to get some kills as a support, especially if you are securing a kill that might have otherwise escaped. You should be fine as long as your kill count isn't higher than your ADC's, unless your lane partner is very unskilled or having connection issues. If someone tries to criticize a support for having a low kill count, it only means that they don't understand how the support role functions, and aren't really worth listening to. Be cheerful and friendly, enjoy the game, and make the most of your limited playing time.
The reason is because it bugged me a bit to here I was to blame for us losing.
