Why do you think the colonists considered themsekves british subjects rather than americans?

Because they were British subjects and they felt loyalty to the monarchy. George III was a little on the insane side, but he was an exception. He angered the people who understood what he was doing and considered it unfair. Had he been more reasonable, he might have prevented war. 

I always tell people to read the Declaration of Independence. It is a short document and very well worded. Jefferson did not write it as a frothing at the mouth rebel. He and the others with him regretted what they had to do but they were firm in their actions.