Exactly how slow is asymmetric encryption?
Yes, asymmetric encryption is slow compared to symmetric encryption. 

With symmetric ciphers, encryption and decryption speed can be several gigabytes per seconds on a common PC core; see these benchmarks.

With RSA encryption, on comparable hardware, we are talking tens of thousands encryptions per second, and only few hundreds of decryption per seconds, for common key sizes, and small messages (like 1 bit to 250 bytes, way enough for a session keys and authenticators); see these benchmarks.

Pure asymmetric encryption would often be like 3 to 5 decimal orders of magnitude slower than symmetric encryption is. That's the main reason why in practice, when enciphering messages that could be over what fits the capacity of a single asymmetric encryption, we use hybrid encryption.