Why on earth would you introduce a character that doesn't care about the party exactly?
Because the character has its own agenda and sees the party as merely a temporary means toward achieving a greater end? [1]
Because the character isn't here by its own choice? [2]
Because the character comes to realize the party, or some members thereof, for whatever reason(s) aren't worth saving? [3]
Because the party are - knowingly or unknowingly - directly acting against the character's interests? [4]
I could go on, but you get the point - there's many reasons a character might come in to a party and yet not care about said party. Examples follow of how each of the above might appear in a game:
[1] - character is seeking a specific ingredient for a magic item and knows it can be found at Dangerous Location X. Character learns the party is going to D.L. X for different reasons, joins up, and tags along without caring about the party (he sees them as merely very talented but expendable bodyguards) or its own mission (in which he has no interest).
[2] - character is a foreigner or alien rescued or found by the party, doesn't know anyone in it, and is more interested in finding its fellow prisoners/survivors/etc. than in helping the party. Or option B: the character has been sentenced or ordered to join the party against its own wishes.
[3] - character is a pacifist, the rest of the party are not.
[4] - character is a staunch royalist, and only learns after joining the party that their mission is in fact to overthrow the crown.
That's just begging to end up in conflict.
For [3] and [4], perhaps. [4] also hints at the classic spy scenario, where the character joins the party specifically to report on and-or disrupt its work agains tthe crown.
For [1] and [2], however, not necessarily so much.