304 contains iron as has been pointed out.

What hasn't been explained is why it doesn't respond to magnet as you indicated.

304 is an Austenitic Stainless. That means its primary crystaline structure is face centered cubic.

This structure does not respond to magnetic force.

In the event that there is some tiny amount of martensite created during a heavy cold work, or there is a small remnant of delta ferrite in the material, a slight attraction to magnetism will be noticed. Cold work is the only way to increase the hardness in 304; as you increase the cold work, I believe that you will lso notice a slight increase in response to the magnet.

But your idea of "its iron so it must be magnetic" is false. The crystalline orientation /structure / arrangement of the iron is also a determinant of magnetic response.

Question back to you for clarity, " if the presumption that "all iron will be attracted to the magnet" is true,why won't putting a strong magnet on your wrist collect and hold your blood at that point? (No humans were harmed by the above human based experiment at the milo household)

Also you may note that above a certain temperature (Curie point) even normally magnetic responsive steels (ie plain carbon or alloy steels lose their response. These steels are ferrite/pearlite or martensite at room temperatures.

I demonstrated this by the following test. I used a magnetically attached temperature gage to monitor temperature in the exit stack of my wood stove. When I had a much to hot fire in the stove (actually, we think we had a bit of a chimney fire) the temperature was so hot that the steel chimney stack got above the curie point and the thermometer fell off.

That told me to get the fire extinguisher and the hoses ready...

Fortunately that was a short lived temperature excursion and was a one time event after we set up a regular schedule for chimney sweeping.

milo