So then would you say that it is a man-made event, rather than a sacrament? We use the word "ordinance" instead of sacrament, but I'm not aware of any significant difference. Baptism is commanded by God, so it can't be man-made.
Would it be like me wearing a crucifix - a man-made symbol of Christianity - rather than something significant in and of itself?
While I have nothing against someone wearing a crucifix, I don't think the two are comparable because God does not specifically command it. When we baptize we do so in specific obedience to God, just as with the Lord's Supper.
Baptism is commanded by God, so it can't be man-made.St. Paul didn't seem all that thrilled about it:
1 Corinthians 1:10-17
10. I appeal to you, brothers, in the name of our Lord Jesus Christ, that all of you agree with one another so that there may be no divisions among you and that you may be perfectly united in mind and thought.
11. My brothers, some from Chloe's household have informed me that there are quarrels among you.
12. What I mean is this: One of you says, "I follow Paul"; another, "I follow Apollos"; another, "I follow Cephas "; still another, "I follow Christ."
13. Is Christ divided? Was Paul crucified for you? Were you baptized into the name of Paul?
14. I am thankful that I did not baptize any of you except Crispus and Gaius,
15. so no one can say that you were baptized into my name.
16. (Yes, I also baptized the household of Stephanas; beyond that, I don't remember if I baptized anyone else.)
17. For Christ did not send me to baptize, but to preach the gospel--not with words of human wisdom, lest the cross of Christ be emptied of its power.