I was in a game Morgana supp with a teemo adc. I get 2 kills because they dive him under tower. He ends up dying then says I need to supp and not steal kills. I question him and he responds with "supports are never suppose to get kills"...
If you can give the adc kills, then ideally you want to give it to them. Marksmen need gold.
If they cant get the kill, then you get it lol
Well... It depends on the situation.
If there is no possible way for the ADC to get the kill then you are more than allowed to take it.
Example: If there is no way to kill a low health enemy without taking the kill and your ADC is dead it's better to give them an assist then let the low health enemy go.
Example: If you're tower dived you want to do as much damage as possible but your ADC was focused and dies. You can do 1 of 3 things.
1: Allow tower to kill a low health enemy and see who gets the kill
2: Focus the higher health enemies to protect yourself
3: Play safe and attempt to go back to base
I'm a support main and I know sometimes it's impossible to allow your ADC to get all of the kills, Especially if you're playing a high damage support like 
or 
Ideally you don't want to get kills; However some situations won't allow you to give yourself an assist without letting the person go.
It is ALWAYS better to try to eliminate the enemy and get your dead ADC an assist then waiting to see if he'll get the kill which has a chance of loosing your lane a kill.
The quote sounds like a narrow minded approach frankly. In a way it's basically saying that should a kill be in sight and your marksman or bot lane partner is not there to pick up for it, you're supposed to disengage. I've been on the side of the "stop taking kills" quote by the bot laner and "why didn't you kill" quote by the jungler once in the same game as Sona. Although that was a rather toxic game in itself from the start and I was quite more in that "I don't give a damn" mindset unlike nowadays.
You did as you needed to honestly. Letting go of those kills would be letting go of gold. Basically you take the kills and he makes that quote. But if you don't take the kills, the player possibly flames you for it. It's better off calling it worth than nothing which is why I think the player's response was very narrow minded and selfish.
Added note: Not just Teemo bot lanes. I'm a Teemo bot lane player. I never really care about having kills taken
