There are already a lot of good answers, but I'll add one slightly different perspective. Since you can't actually build a perpetual motion machine, when people claim that one such machine works, they are always making theoretical arguments. Those arguments usually invoke basic results in physics, such as the forces between magnets, the buoyant force, torque balance, and so on.

However, those results in turn are derived from the basic laws of physics, and from those laws, you can also derive that energy is conserved! So the argument saws off the branch it's standing on.

If you think about it, there are only four logical possibilities:

1. The known laws of physics contain an internal logical contradiction. It would seem very unlikely for nobody to have noticed this, especially because these machines are often made of very common parts, like magnets and ropes.
2. The machine exploits a violation of the known laws of physics. We can usually ignore this possibility because perpetual motion machine designers assume the laws of physics work in order to argue their machine works in the first place. Sometimes machines do violate the known laws of physics, but in that case they're not machines, they're physics experiments discovering new effects. Generally, such experiments are rare and difficult, and unlikely to be built in some retired engineer's garage.
3. The machine works, but only by using some other source of energy which its designer didn't account for. A lot of "working" perpetual motion machines actually just inefficiently harvest solar energy, or the Earth's rotational or magnetic field energy, or something else like that. These aren't interesting because they're usually extremely uneconomical compared to other energy generation mechanisms, like solar power or nuclear power.
4. The machine doesn't work.

Physicists dismiss perpetual motion machines because the first two options are exceedingly unlikely, and the last two are boring.

There are already a lot of good answers, but I'll add one slightly different perspective. Since you can't actually build a perpetual motion machine, when people claim that one such machine works, they are always making theoretical arguments. Those arguments usually invoke basic results in physics, such as the forces between magnets, the buoyant force, torque balance, and so on.

However, those results in turn are derived from the basic laws of physics, and from those laws, you can also derive that energy is conserved! So the argument saws off the branch it's standing on.

If you think about it, there are only four logical possibilities:

1. The known laws of physics contain an internal logical contradiction. It would seem very unlikely for nobody to have noticed this, especially because these machines are often made of very common parts, like magnets and ropes.
2. The machine exploits a violation of the known laws of physics. We can usually ignore this possibility because perpetual motion machine designers assume the laws of physics work in order to argue their machine works in the first place. Sometimes machines do violate the known laws of physics, but in that case they're not machines, they're physics experiments discovering new effects. Generally, such experiments are rare and difficult, and unlikely to be built in some retired engineer's garage.
3. The machine works, but only by using some other source of energy which its designer didn't account for. A lot of "working" perpetual motion machines actually just inefficiently harvest solar energy, or the Earth's rotational or magnetic field energy, or something else like that. These aren't interesting because they're usually extremely uneconomical compared to other energy generation mechanisms, like solar power or nuclear power.
4. The machine doesn't work.

Physicists dismiss perpetual motion machines because the first two options are exceedingly unlikely, and the last two are boring.

Another important factor is that it tends to be exhausting to debate the designers of such machines. It's usually pretty obvious, even to people without physics training, that a simple machine won't work. Most people just give up there, and the ones that don't are those who psychologically need their idea to work. They simply tack on more and more complications, until they can no longer tell at a glance that it doesn't work, and then triumphantly claim that it therefore does work. Not only does this complication make it hard to analyze their machine, but once you disagree, they simply add another complication and declare that the new machine must work. The process repeats forever, because these people are only interested in ways they can be right, rather than considering the possibility that they're wrong.