The difference is that if you're sending your specimens out under client billing, you're not reading the slide (professional component) or creating the slide to be read (technical component). Even if you read all your slides and billed for the PC, do you expect that a lab would make you the slide (TC) for free? When you send a biopsy to a pathologist/lab, that lab is spending a lot of money in order to be able to make those slides in the first place (capital input for all the supplies, machines, processors, staff to gross and process the slides, embed them, cut them, stain them, etc. The lab/pathologist group probably also pays for all those nice little formalin jars you submit your biopsies in as well as pays a courier to come and pick up your biopsies. So you're not just paying a pathologist to read a slide you could read yourself. If you hired a dermpath, you'd still have to "buy" the technical component from somewhere if you want your tissue to be turned into a slide.
As a complete aside, I'd like to know how strongly dermatologists would support client billing if the tables were turned. If every PCP or referring doc expected that a derm would turn over 40% or 60% or 80% of the reimbursement generated from their derm exam (including any reimbursement generated for the office visit, procedure codes, etc) for every single patient that got referred to them from another doc every single time they saw that patient, would they be just fine with it because "without the referring doc the derm wouldn't get that patient anyway?" Of course, for many reason this isn't the way things work, but I think it would be interesting to consider.
Finally, I just want to make the point that client billing is not about derms vs pathologists. Many groups of clinicians--derms, GIs, uros, OBs, engage in client billing practices, and in many states, these billing practices are legal so these docs are not breaking the law. Derms are not solely responsible for the forces that have allowed client billing to come in existence or that allow it to continue. But most derms who engage in client billing should call it for what it is, which is free money earned off another physician's work.