Franklin, in Poor Richard's Almanack, is cautioning against considering a new acquaintance as a friend in haste, and moving even more slowly in loosing a friend once one is found.
A true friend is thoughtful, compassionate, interested in sharing good and bad times and experiences. Friends care for each other, are loyal and trustworthy, and protect each other from disappointments or injuries whenever possible. Such relationships are difficult to find and it takes time for one person to demonstrate that s/he is willing to fulfill these roles for another. Therefore, considering someone as a "friend" is something that should be done slowly.
Once the relationship of "friend" is established and proven, however, it should be treasured and sustained. Changing friends involves taking the risk that a new friend might prove to not have the qualities of an old friend. Because of that risk, making a move to change a friend should be approached very slowly and thoughtfully.