I'm sorry, but this is one of the dumbest things I have ever heard suggested.
If more guns prevented violence, then the United States should be one of the safest countries in the world because we have more guns and gun ownership than any other civilized "first world" country on earth. Perhaps at birth, we should replace giving children one of those small stocking caps to instead tether on a .25 caliber semi-automatic pistol. As they age, we could replace it with a .357, perhaps a 9mm...hell let's add an assault rifle so they can have total safety on the playground.
What has not been discussed in the news (and the police chief touched on it when questioned), is whether any of those killed in Orlando died from "friendly fire." There were guns in that club -- off duty police officers provide security at most Florida bars and clubs. They are armed with the weapons they carry on duty. They are trained. And yet it did not stop this event. The same happened, by the way, in California when the 14 were killed. There were two people who were armed and had concealed weapons permits that hid and protected themselves until the killers fled.
When the shooter in Orlando ran to the bathroom, he ran along a cinder-block wall. If anyone has any brain at all about shooting in rooms with cement walls, they also know that bullets don't stop; they ricochet until their energy is expended or they find some other object that stops forward motion. So lets throw a bunch of guns in schools with the same types of construction and have a shootout. Yeah...that works.
The other problem is that responding police officers now have to identify shooter from victims. The Orlando shooter actually tried to hide among the victims until discovered. Imagine rolling up on a scene with 250 people fleeing doors and everyone having guns and shooting. Who's the bad guy? The assumption then has to be that EVERYONE is the bad guy and it only prolongs the time that help can actually intervene.
What angers me most about the current "lack of" debate is that everyone says legislative solutions would not eliminate every mass shooting. They are right. After 9-11, I have to take my shoes off, practically strip at the airport, have my lube confiscated (if over 3 ounces), and walk through various detectors. And yet we have still had bombings of planes and other incidents. Nothing we do has any guarantee (hence the many shootings in Chicago). But to throw up our hands and say "get everyone a gun" is absolutely mind-boggling and irrational.