The exchange is grammatical, but the tone of B's response is questionable (with or without "on"), like B is annoyed at being asked and is answering sarcastically. Also, beginning a sentence with "Honey" in a situation like this sounds antagonistic.
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Anonymous, I'm not sure whose answer I should accept as a correct one.Hmm. Difficult choice.
fivejedjon Anonymous, I'm not sure whose answer I should accept as a correct one.Hmm. Difficult choice.CJ is a teacher and a moderator of this forum. He has posted nearly 68,000 responses over twelve years. The other has posted their response anonymously. Do yo really need me to confirm that CJ is right? ps. The 'on' is not essential in BrE.Who's CJ? You mean
AnonymousB: Honey, I am on any day you want me to be.It seems that it should be "I am free on any day you want me to be."
AnonymousWho's CJ? You mean Clive?Sorry. I have now corrected my slip.
Anonymousit seems that you don't stand behind the anonymous answer.I don't.
fivejedjonSorry. I have now corrected my slip.Glad that this wasn't something that I did not understand.
fivejedjonI don't.Thank you for the confirmation. Appreciate it.
khoffIt seems that it should be "I am free on any day you want me to be."Might I ask why it should?
AnonymousMight I ask why it should?It is partly because in this conversation, omitting 'free' leaves only 'I am', which is a very vague statement. In other dialogs, omission of the adjective is more likely: