We say "two's company; three's a crowd" because sometimes two people are having fun together and would not have as much fun if a third person joined them. Example: "I hope he does not come over to our table; two's company; three's a crowd." "Company" here means people who have been invited; they are relaxed and comfortable together. A "crowd" is an uncomfortably large group who's size cannot be controlled. "Two's company; three's a crowd" says that a group of two people is more comfortable than a group of three. Example: "I was hoping just you and I would see the movie. Why did you have to bring your sister? Two's company; three's a crowd!"