Who's making coronavirus testing kits? why are they so limited in supply and so hard to make?

Many suppliers: The PCR is a technique of molecular biology that involves the mechanism of replication of the DNA. They look to reproduce several times from strands of viral RNA, certain regions of it in order to know that is certainly that virus. It involves also the use of an enzyme that allows the technician to replicate that certain part of the RNA. In order to do it you need extensive training and equipment.

COVID 19 testing: The FDA has a list of test kit manufacturers and commercial laboratories at https://www.fda.gov/medical-devices/emergency-situations-medical-devices/emergency-use-authorizations#covid19ivd. Why are they so limited- because we simply were not prepared for a major pandemic and the surge of patients.