H1 Process cycle

I am negotiating with one of companies for starting date. I want to start in June. but HR sent email to R&D manager and said as folows:

HR's email to R&D manager:

"Would you consider waiting until late June? He would then only require 6 days out for the balance of the year. Drawback is that if we wanted to file for an H-1, we would be late in the visa processing cycle."

my questions is why HR said it would be late in H1 process cycle if I start the late of June?

Thanks a lot