Made pretty self-evident by how their confrontation is framed by the manga itself tbh.
This part :
The moment Sentoumaru said that he doesn't care what side he is on as long he protects the old man he owes his life to (who is now an enemy of the WG) Kizaru starts being reminiscent of their first meeting :
The following panel is when he made peace with the fact that the mind of the kid he trained was definitely set and there was no going back. This felt like a farewell :
Before that scene he was roughing up Sentoumaru, showing him it was hopeless, but was still having the faint hope he may give up seeing how outmached he was. (Hence why he said he should surrender and asking why he was getting chummy with pirates)
Which is reason why he suddenly and mercilessly packed him up 5 seconds after this scene and later said he wished he could add "old friend" as things he was ordered to protect. Oh well, Sentoumaru made his choice. His job is more important than personal relationships