As has been cited above, this is absolutely false. The case law is cited. As a courtesy to your friends in law enforcement you may want to educate them on the law in Wisconsin. The City of Racine was sued by Wisconsin Carry for arresting one of our members for obstruction for merely refusing to give their name. A judgement of 10,000 was entered against Racine for this illegal arrest without probable cause. Its frightening that those in law enforcement do not know the law.
Racine had to learn the hard way:
http://www.youtube.com/wisconsincarry#p/a/u/1/PuiO8tixuKY
If you want to show them your ID just because they demand it, thats your choice.
As to what is wrong with showing them.
If you have done nothing wrong, why should you show them? This is not a police-state. Citizens are not assumed to be guilty. We have a right to privacy. Police have a duty to follow the law. Why shouldn't you just show police your ID upon demand. Because we are FREE PEOPLE. Freedom means you don't have to show ID to law enforcement just because THEY demand it.
Freedom means that the police do not get special powers over law-abiding citizens just because they are police.
Freedom means that police are JUST people, no more or less than you or I, and they have no more moral authority to demand your ID (if you are not breaking the law) than you have moral authority to walk up to a stranger on the street and demand their ID.
If those principled reasons why you shouldn't show police your ID are not enough here are some practical reasons:
Police are human... they have prejudices and grudges, and personal issues just like anyone else. Because of the authority their job gives them against criminals, it could be VERY tempting for them to misuse that authority against the law abiding. Maybe the police don't like how I look. Maybe they don't like that I carry a gun. Despite the fact that is all legal, I don't want to give the police my name so they can find out where I live and perhaps wait for me to leave my house and give me "special" attention for driving a couple MPH over the speed limit.
When I've done nothing wrong, I don't want the police to have my name so that if I run into an arrogant cop who doesn't support the right to keep and bear arms he doesn't go back to the police station and say to all the other cops "yeah, that Nik Clark that lives over on xyz street was a real ass" (just because I open-carry) and have the rest of the police know my name and have that ONE officers personal judgement of me (which is just his own perception based on his personality and his disposition at the moment he interacted with me) imposed on other officers who could decide to run my name, see what I drive and harass me for minor traffic infractions.
By knowing and exercising my rights, I'm not enabling the police to overstep their authority. Despite doing NOTHING wrong, if I exercise my right to not give my name, I'm letting the police know the limits of their authority. (sounds like your friends need to be reminded of this) History shows us that rights unexercised are rights lost. This just encourages the encroachment of tyranny.
Its very important that police abide within the law, not outside of it. Its very important that police don't get to assume authority that the law doesn't allow them to.
If we let police assume authority that the law doesn't allow them to, what good is voting? What good is electing representatives who will go debate laws and debate the limits of the law and the limits of police authority? If we just "do what police say" despite the fact that the law doesn't provide them that authority, we are ENABLING them to assume powers they don't have by law. That skips the legislative process and removes the ability of the people to have a say in the laws they live under.
We are suppose to have a government OF the people BY the people FOR the people. Not a government of the police, by the police, for the police.