Overwatch Is a Squad-Based Shooter
It’s easy to get caught up in all of the excitement during an Overwatch match. You may get carried away and leave your post to chase down an opponent, and that’s exactly what they want you to do. Each character has a role on the battlefield, and when using them for that role you will get the most out of them.
Support characters are able to kill just like any other character, but they are best when kept back away from battle so that they can keep offense-focused characters in the fight. Leaving your post while a battle is going down can easily lead to your team being wiped out, just because you, the support, stepped away.
Overwatch is not a game that only rewards the person with a lot of kills. You can get no kills whatsoever and still be just as important as the player who got them all. You can only win as a team, remember that.