Why does TCP header contain both ACK and SEQ fields?

Question

Since TCP header is a relatively large overhead, why don't we compress it in the way that ACK and SEQ share the same field, and they can still be distinguished by flags in the header?

Answer 1

Because they can both be present in a header at the same time. One is for tagging the data being sent, the other is what the sender is expecting in the next packet back. See wikipedia for more information.

Answer 2

Because the connection is full-duplex - one sequences packets to the peer, the other acknowledges packets from the peer.