In a few places, Monroe seems to want to make it look like Americans are really rooting for Europe. It's probably a way to be diplomatic and not too aggressive, given that he's taking a stance against several countries larger and more powerful than his.

Also, the U.S. was very actively trading with Europe, and needed to maintain a good relationship with those countries. It was just good diplomatic sense to take a "Hey, buddy! You look great? Have you been working out?" stance with to Europeans.

So, when Monroe talks about how Americans "cherish sentiments the most friendly in favor of the liberty and happiness of their fellow-men on that side of the Atlantic" (8), or the existence "the amicable relations existing between the United States and those powers" (14), he's emphasizing the existing goodwill between the two regions. (He's also probably lying through his teeth, but oh well—that's diplomacy sometimes.)

When Monroe casually mentions the decades of power struggle that have consumed Europe, he talks about how America has been happy to work with any and all kings, emperors, and parliaments, "to cultivate friendly relations with it, and to preserve those relations by a frank, firm, and manly policy" (21). He tries to soften the bold stance of the Monroe Doctrine's main points by reminding Europe of how accommodating (and manly?) the U.S. has been, and how supportive its people are of their European bros.

Whether or not that's true, we can only guess. Unless you've finally finished that time machine, in which case, there's a whole other discussion we need to have. For now, we'll have to be satisfied in the use of the friendship motif in the Monroe Doctrine as a device to put the U.S. in a positive light…even when they're potentially threatening the global balance of power.