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I get how standing wave patterns are created in strings: At a certain resonance/natural frequency of the string, a standing wave is created, increasing the amplitude of the sound, and standing waves are created in the string.

However, for open-open and open-closed tubes, the anti-nodes and nodes are represented with displacement-position graphs or pressure-position graphs, and how they are actually formed physically inside the air column is hard to picture.

My teacher told me that they are a result of longitudinal pressure waves (sound waves) reflecting from either closed or open ends to set up standing wave patterns, but I do not see how they can "reflect" off of an open end.

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Acoustic waves reflect off of open ends because right at the open end, there is a sudden impedance discontinuity, and anytime you have one of those, you'll get a reflection of the impinging wave.

It's easy to visualize this for the case of a tube with a closed end, which represents an extremely high impedance: the incoming pressure wave piles up against the immovable wall at the closed end and bounces back off it, like a water wave hitting a sea wall. It's harder to visualize this in the open-tube case but I will try here:

It's easier for an acoustic compression wave to propagate through the open air than it is for the same wave to travel down a tube. This means that when the compression wave going down the tube encounters free air right outside it (lower impedance!) the wave eagerly departs and disappears into the open- the opposite of the case when it hits a closed end.

Now you have a situation where the departing wave tries to pull a little extra air out the open end of the tube with it, and the rest of the air inside the tube is being stretched- and therefore pulls back- and part of the wave then snaps back inside the tube, going the opposite way.

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The energy in a wave is shared between kinetic energy of moving media and potential energy due to some restoring force. The balance between them is important: if it changes at some point, the propagation of energy is disrupted.

A closed pipe is similar to a fixed end to a string: there’s no motion there, too much restoring force, hence a reflection.

An open pipe is like a free (I.e. cut) end of a string: there’s no restoring force, so all the energy goes into kinetic. In the string case, this is because there’s no next piece of string to pull down, and the free end moves a lot. In the pipe, an open end means the pressure wave can expand out in many directions, without the pipe to confine it pushing just back and forth. The energy goes mostly into motion, not compression/expansion, so there’s a reflection.

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