FreeBSD's kernel is smaller and more cohesive than Linux's. The whole OS (kernel and userland) is developed as a single project, whereas Linux is just a kernel with a massive and fragmented contributor base. When you need to make deep cross-cutting changes, like modifying how sendfile interacts with TLS interacts with the TCP stack interacts with the NIC driver, that's way easier in a smaller, coherent codebase.
Netflix's CDN nodes are basically single-purpose appliances that do one thing: push video bytes to your screen as fast as possible. For that kind of workload FreeBSD's network stack was historically stronger, and the codebase was easier for a small team to reach into and tune aggressively. They've gotten individual servers past 100 Gbps of TLS-encrypted traffic. A lot of the optimizations they needed (kernel TLS offload, sendfile improvements, custom TCP tuning) they built themselves and contributed back to FreeBSD, and the kernel's size and structure made that practical in a way that would've been harder in Linux.
The other piece is licensing. BSD license is permissive, GPL isn't. Netflix wanted the option to make deep kernel modifications without being required to open source everything. They ended up open sourcing a lot of it anyway, but having the choice mattered.
Worth noting they only use FreeBSD for the CDN. All their backend services, recommendations, control plane, that's all Linux on AWS. So it's not that they rejected Linux, they just picked FreeBSD for the one job where it had a real edge.