Why an American war with Britain in 1861 could deepen division

What if the United States attacked Britain in 1861 to encourage unity between the Northern and Southern states?

The war could worsen internal divisions and draw in European powers rather than preventing the American Civil War.

A war of aggression against Britain would not guarantee support across the Northern and Southern states. Early losses could intensify internal political conflict and make the attempt at unity embarrassing. Britain could also gain French or German support because both powers had interests in Mexico and the wider region. Royal Navy control of transport would then allow European forces to appear in North America, turning a domestic political gamble into a much larger war.