Probably the better question is why doesn't Mr. Darcy have warm feelings towards Mr. Wickham! That's a whole seperate kettle of fish however.
Mr. Wickham claims to Lizzy to not have warm feelings towards Mr. Darcy because after Mr. Darcy's father died, Mr. Darcy threw him out penniless. Mr. Darcy's father had been fond of Mr. Wickham (according to Mr. Wickham) and had planned to provide for Mr. Wickham so that he may join the ministry. Instead, penniless, he was forced to seek his fortune in the militia.
Mr. Wickham is also known to be a charming man, unlike Mr. Darcy, but does charming mean that he is a better man than Mr. Darcy? Keep reading! You'll find out!