Where to start? First, if you didn't do anything wrong, many people feel like they can talk freely to the cops...because they didn't do anything wrong. Now, that may sound stupid to those of us in the know, but most people are not in the know.
Second, you don't think you did anything wrong because you weren't involved in the situation.
Third, you were a part of the situation, but being a good citizen who thinks you acted within the law, you feel like providing your side will help the hard working cops get their job done quickly and you will be home in time for dinner.
Fourth, you heard and understood the words, but you believed the cop, as a person of authority, when he said Mirandizing you was just procedure, nothing to worry about.
Fifth, as a good and concerned citizen who was actually involved, maybe just a witness, you are hoping to help the hardworking cops get the correct story so that they can arrest the correct person.
Sixth, as a lying, cheating, scumbag, you are hoping to misdirect the the moronic, flatfooted cops and pin the crime on somebody else.
Seventh, true story that occurred with a buddy of mine, you grew up believing the cops are all good people and that you always cooperate with the cops.
Eight, some people have heard Miranda so many times, they don't actually process the seriousness of the meaning. Those are just words of formality like, "Hi, I am Officer Justice and this is my partner Officer Slaughter." (I actually met these guys)
Nineth, you are young, inexperienced, intoxicated, stoned, in mourning, in shock, in physical injury pain, etc. and not actually capable of processing the significance of the situation you are in at the time, unlike somebody who may be older more experienced, clear headed, didn't just see their spouse gunned down next to them, uninjured, etc. and fully capable of making proper decisions in situations of extreme significance.
That is about all that I can think of, offhand, but you would have to ask the thousands of people each year that opt to cooperate with the cops when they should be requesting a lawyer and otherwise keeping their mouths shut. Maybe you could ask
IJ1981 why.