I.... I mean technically you're wrong. But you're still wrong. Everything is magnetic in some form or another.
And the magnetism of iron ions are the same of metallic iron: paramagnetic.
metallic iron has six 3d electrons, two paired and four unpaired which means it is paramagnetic.
the iron in your blood is found in the heme protein iron (II) with six d electrons, two paired and four unpaired (though it's missing both of its 4s electrons)
Both forms of iron exhibit the same form of magnetic susceptibility as each other.
So if you did indeed have a block of crystalline hemoglobin that block would be attracted to the magnet because of its iron content, so that's exactly why you're wrong. Granted the amount needed would be almost 1.356x that of the magnet in this article for it to be pulled directly from your blood, but thats beside the point.
When hemoglobin is dissolved in a red blood cell the situation is a slightly different. the heme will hydrogen bond with the liquid in the cell, which obstructs its lateral movement, kind of like a golf ball falling through a vat of Canadian syrup. Iron is only about 1/3 % of Hb by mass, so what you have is a very tiny human dragging a very large rock through a very thick syrup. A magnet would attract the iron in blood, however because of the pressure in the vessel exerted by other forces it would be swept away along with the blood vessel. That is why if the iron content was increased to above normalized levels in the human body it would have a greater chance of pulling the iron out, because the greater surface area to pull from would start to negate the pressure of blood flow (though with this powerful of a magnet you'd possibly die from poisoning first as a human body couldn't withstand the amount of... "polution" of having that many iron ions in your blood. The normal concentration of iron in blood is 60-170 ug/dL, or 6-17 ug per cm^3 blood. The density of metallic iron is 7.9 g/cm^3. basically, any given volume of metallic iron has about a .88 times as many iron atoms as the same volume of blood. In a 1 cm cube of blood, you'd have the equivalent of a lump of iron the size of a slightly goliathic-bacteria dissolved in the cube. So the magnetic force exerted to pull say a 1 ounce block of iron would needed to be increased by about 10,000 times (give or take a few thousand) to pull the Hb out of your body. OR... you could already achieve this by a semi complex array of magnetic structures, but then the human would definitely die.
Finally, the motion of the hemoglobin molecule would reduce the attraction. It rotates and moves within the RBC in varying ways, meaning it is attracted and repelled by other molecules nearby. A magnetic field would turn the Hb molecule so that the magnetic field of the iron atom is aligned with it, but intermolecular interactions between the Hb and other molecules "bumps" the Hb so that the Fe is sometimes turned the "wrong" direction in the field. The more often Hb is bumped and turned, the less effective the field is at attracting the Fe. At the so-called Curie temperature, the effect of the field is completely buried by the random motion. Hb-bound Fe++ isn't complete immune to the field, only less affected by it than it would be at a cooler temperature or in a less concentrated chemical environment.
So basically you're wrong. And I explained science-like exactly why you're wrong. So please I understand that while you may be interested in science and other things complex, do not misinform individuals based upon a introductory course of biology and/or physics. If I had the resources I could easily rip out the iron in a humans blood, it would just be impractical and quite honestly fucked up to do so. I mean basically what you're doing is pulling all the hemoglobin out, as the amount of ACTUAL magnetic force to separate an iron ion from its familial blood brethren would be about 3x greater than the amount needed to pull the heme out of you.