I'll argue that it was avoidable. Although there were many unresolved issues between the British and America by 1812, and tensions over impressment were running high, the Napoleonic Wars were nearing a successful conclusion for Britain and her allies, and one could easily argue that the British were quite tired of fighting, and paying for, long overseas wars.
With intensive diplomacy, and some compromise on both sides with regards to freedom of the seas and the Canadian border question, it was possible that the War of 1812 could have been avoided. Especially given the fact that little could be settled by war, and both sides knew that even as they began to fight in this conflict. So given a reasonable way out of war, I believe one side or the other would have taken it.
I'll go with destined here. (Of course, all wars are avoidable, but only if the countries involved are willing to act in ways that won't bring the war on. They often fail to do this.)
The reason that it was destined is that Great Britain was not completely resigned to the idea that the United States was an independent and sovereign nation after the Revolutionary War. Because the British felt this way (and because they were not happy about having lost the colonies) they continued to act as if the US was still a colony. They stopped US ships and forced American sailors into the British Navy as if they were still British citizens. They kept British forts on US territory as if it were still British.
Because the British were not willing to let go of the US completely, and because the US was sure to push for Britain to recognize its sovereignty, the war was destined.