Because the antibiotic automatically selects the successful clones. The others that didn't incorporate the plasmid don't grow into colonies. Without antibiotics

Because the antibiotic automatically selects the successful clones. The others that didn't incorporate the plasmid don't grow into colonies. Without antibiotics your plate will be entirely full of bacteria, you can't pick individual clones from that. And you want clones, so all identical bacteria derived from a single successful integration of your plasmid into a bacterium. You don't want a mixture of bacteria with different DNA. This process isn't perfect and you need to screen out cases where your DNA sequence is not correct. And by far the easiest way to do that is to grow on plates with antibiotics, and an amount of bacteria that results in a few individual colonies, with each clone being full of genetically identical bacteria. You generally want antibiotics in your media anyway, working without antibiotics makes it much more difficult. You don't have 100% perfectly sterile conditions, with antibiotics you have a much larger margin here.