I bought an electromagnet online hoping to make it attract and repel metals by changing the polarity of the voltage on it, but I ended up experiencing attraction all the time.
Is there any way to make an electromagnet that attracts in one way and repels in another way?
For a magnet to repulse something, that something needs to also be magnetized and the like poles of the two magnets aligned.
The electromagnet attracted everything magnetic because those other things weren't polarized with their own magnetic fields. Two electromagnets, or the electromagnet with a permanent magnet would work.
A coil that is energized with alternating current will repel a conductive but not magnetic ring.
Reversing the polarity on an electro-magnet will reverse its poles but it will still be a magnet.
simulate this circuit – Schematic created using CircuitLab
Figure 1. Reversing polarity on electromagnet reverses poles.
Thought experiment: if you had purchased a bar magnet and found that one end of it attracted metals, would you have expected the other end to repel?
Figure 2. Unlikes attract. Likes repel.
It is possible to make an electromagnet repel a permanent magnet. To accomplish this the electromagnet's current needs to induce a magnetic field "He" in the core which is stronger then the opposite field Hm that the magnet is inducing on that same core. If |He| > |Hm| then the core is magnetized by He-Hm, a net field whose polarity depends on the direction of the applied current. Normally a pretty strong current is required to overcome Hm, making it appear that the magnet always attracts the core.
