I would like to think that if the Founding Fathers chose to initiate a war with Britain over Ticonderoga they would have done it for a reason more substantial than 'just a matter of pride.' Several hundred thousand dead seems like a high price to pay for something as petty as that.
Apparently it wasn't. They surrendered it, if you will remember. But the point remains, why should you need to defend a Fort that is not in your own country?
From the viewpoint of Anderson and his men, the fort was in their own country.
You need to study history more. In the beginning, no one thought it would ever grow so large. Both sides thought they would do a little ass slapping, and that would be that. Each one underestimated the resolve of the other. The Confederates had already taken over many other forts, yet none of these were regarded as a Casus belli. Lincoln himself was of a divided mind as to whether he should relinquish the two remaining forts, and went so far as to poll his cabinet regarding what he should do.
It was a real possibility that Lincoln could have simply turned over the keys and walked away from this conflict. I don't know that History would have turned out better had he done so, but I'm pretty sure it would have saved over 600,000 lives.
From the viewpoint of Anderson and his men, the fort was in their own country.
When we broke from the British we sent them a Declaration of Independence. At that point, what was formerly the property of the crown, became the property of the United States. Do you want to claim that it remained British Property?