The head of the British GCHQ said that us companies such as twitter and facebook have become the commmand and control centers for terrorist groups. Does that mean that the u.s supports terrorism? Of course not.
Social media websites aid terrorism, claims GCHQ chief - HITC Tech
Many of the isis terrorists came from western countries so that means that they had to travel in western countries and go through their security to get to turkey from where they go to syria.Does that mean that those western countries where the terrorists came from are supporting isis? Of course not.
With regard to kobani/ayn al arab:
Right across americas border in mexico there is a drug war going on where between 80k to 100k people have died. Many of these deaths occur in border towns right across the u.s border. Should the u.s send troops into mexico to stop this violence? I say no because the u.s has already taken in millions of refugees as immigrants from mexico.
Another point i want to make is that the cartels are going back and forth across the u.s border. Does that mean that america supports the drug cartels? No it doesnt.
The cartels are violent like isis. They chop off heads and do mass executions, they also sell women into prostitution. But that doesnt mean that the u.s is obligated to send troops into mexico.
(Kobani was called arap pinar in ottoman times then syria changed it to ayn al arab, and now kobani the unofficial name is being used)