Ideally it should be agreed on, but DM has the final call
When the rules are vague (intentionally or not) the DM gets to decide how to fill the gaps.
Suggestion contains no wording that suggests a measurement for "reasonable" nor who would judge that. Therefore, the DM has the final call. However, making unilateral contentious decisions without consideration of the player will lead to no fun and lots of trouble.
Before I dive into that, I want to challenge something very important that you said in your question:
This is not an issue of player agency
Mind control spells take away player agency by their very definition. Their point is to control a PC's actions to make them do something you want them to do. This is removing agency and it is 100% legal and part of the game. There is no way to have mind control while preserving player agency so that is not the issue for this particular question.
DM and player should talk it out (and trust each other)
The first thing to note is that this isn't a negotiation per se, but the fact is, the player may have a valid objection to what is "reasonable" to their character and hearing that out will be beneficial to everybody. Defining what is "reasonable" is something that I am not going to dive into because it is not relevant to the question (and already has a Q&A covering just that).
When I DM, unless it is blatantly obvious (DM & player agrees), scenes like this usually play out as a short dialog between me (the DM) and my player. I tell them what the suggestion wording is and ask them how their character reacts. If they object (as in your scenario) I'll ask them to explain briefly why their character finds the suggestion absolutely unreasonable. If I find their answer compelling I let the spell have no effect. Otherwise, I'd rule that the spell takes effect and explain my reasoning if necessary. The ruling should focus on what the character would or would not find reasonable.
As DM, it is important to listen to your players and to assume and trust that they are earnestly telling you something important about their character.
However, as a player you must also trust that the DM (hopefully) has a bit more of an unbiased view of your character (eg is probably not as bothered by bad things happening to them as you are) and allow the DM to make the final judgement.
If there is mutual respect and trust at your table, this interaction becomes on average much easier.
A great way as a player to build up Player-DM trust is to accept the DM's suggestion without a fight in cases where it really makes sense (even if it likely works against your character). A great way to reward and encourage this is to award advantage to players who do this for staying true to character, especially if they really follow the spirit of the spell (as an enchanted character would).
As a DM you can build trust by recognizing when/if you made a clearly unreasonable suggestion and not fighting the player/character when they point it out. Always remember that enemies do not necessarily know or understand PCs in a way that would allow then complete accuracy when casting suggestion. Even a spell failure can be a successful storytelling moment. Also, by being judicious in your use of mind control spells to begin with. They can feel unfun and unfair even to the most sporting of players if used in certain ways.