It was a civil war. Tens of thousands of American colonists served in the British Army in Loyalist regiments (Hugh Bicheno's 'Rebels and Redcoats' states that more were serving with the British at the end of the war than in the Continental Army! - although I'm dubious of his claims as he writes more like a popular historian than an academic), American politicians such as Benjamin Franklin's son and Joseph Galloway took the British side even after war broke out, some American generals like Arnold defected to the British, the Continental Army had a smattering of formerly British Army generals and officers, between 20-33% of the population were Loyalists depending on the source you believe. There were a number of battles fought that had minimal to no British/Continental Army presence such as Moore's Creek Bridge or King's Mountain - these were explicitly battles of American colonists fighting American colonists, in many cases closes neighbours, in the Southern theatre in particular militias of both sides went around burning their neighbours houses and hanging their enemies to settle old scores and further their side's aims, for your Francis Marrions (the 'Swampfox') you had Loyalist equivalents such as David Fanning, when the war was over c.60,000 Loyalists and 15,000 slaves left the colonies permanently due to their side having Lost (Maya Jasanoff, 'Liberty's Exiles'), those that remained were subject to various state laws taking their land and property and preventing them from voting, the Native Americans of the Six Nations split over supporting the British or the Americans etc etc.

The reason why it's not remembered as a civil war is due to the historiography and the necessary nation building myths that came into being after the Revolution. The Americans needed national myths to base their conception of their self upon and didn't want to deal with the issue of a messy, very bloody civil war, so the role of the Loyalists was ignored (it helped that many had left the new United States and those that remained had been expropriated of their property - there was no one left to fight for their version of events and certainly no one with influence) and they rarely figured in the telling of the story until the last few decades when a good deal of scholarship regarding the Loyalists has emerged. Even today the teaching of the war in American schools tends to pass over them. It is far easier and far more in being with the Founding Fathers conception of themselves, their politics and the nation they wanted to create to tell a story of the rights of man, the fight against an autocratic uncaring monarchy from abroad, the political struggle and the revolution of ideas that it represented, the valiant fight of the farmboy who left his hometown for the first time in his life to take potshots at redcoats at Lexington etc than tell the story of a confusing bloody political separation in which many of your neighbours may have supported or had hidden sympathies for your enemy. In essence the losers don't write history, especially when so many of the founding myths of your nation are rooted in such a war.

On the other side the British public simply forgot about the war, it was never a popular war and was soon forgotten in favour of Napoleonic victories and the creation of the 19th century Empire based upon the new style of colonialism. Interest was limited and there was nothing to be gained in challenging the emerging American conception of the war. With their primary benefactors ignoring them no one was left to tell the Loyalist side of the story and thus they're largely forgotten from the popular conception of the war leading to a lack of understanding of the fact it was a civil war, even in Britain itself, where Washington is an order of magnitude better known than the likes of Howe, Burgoyne and Cornwallis, let alone the Loyalists.

You might want to check out Alan Taylor's new book, American Revolutions. He frames the war as a civil war within the colonies.

The American colonies were expressly a subservient part of the British Empire. Americans held a distinctly different level of citizenship (at least while living in the colonies) than those who lived in, say, England. And local officials (elected or otherwise) were not of the same stature as British officials. Most especially, the colonies had no representation whatsoever in the British parliament. One might say "well, many Americans were English or descended from the English" which is true, but it's just as true to say that many Americans were of German, Dutch, or French descent, among many, many other ethnicities. Additionally, if the colonies had been granted parliamentary representation and the rights due every British citizen there likely would not have been a revolt.

Moreover, the revolution did put at risk the British home government, nor was there fighting on British home territory. The explanation that fits the mold more than anything else is one of a revolution for independence.