I wonder why SDS PAGE electrophoresis must be performed vertically and not horizontal as DNA gels?

Might be because SDS-PAGE has two "fused" gels - a loading/stacking layer and a running/resolving layer. On the other hand, agarose gels are homogenous gels, where, in horizontal mode, DNA runs (or "wiggles") along the bottom of the gel. Incidentally, you can purchase "vertical" precast DNA gels too!

i am pretty sure it's because of several reasons. first, the use of the combination of stacking and separating gels. also, the vertical set-up allows for a much smaller gel volume, which is useful when making a denaturing gel which has several toxic ingredients which are also alot more expensive than a simple agarose gel for DNA. additionally, the SDS-PAGE gels only polymerize in the absence of oxygen, so they would never work in an open slab gel configuration.

There is absolutely no reason why SDS-PAGE gels cannot be run horizontally. Indeed we have done it many times. the limitation is that the polymerization process requires anoxic conditions and therefore the gel is best set between two plates sealed from all sides and then laid horizontally after seting and sample is electrophoresed. Alternatively, the gel can be poured on a horizontal gel support but polymerization can occur only under N2 atmosphere in a dessicator in which case, unfortunately, the gel surface may not remain even. Furthermore, one has to use a novel sert of combs to set sample wells.
In any case, SDS-PAGE, or any Polyacrylamide gels in native, urea, acid-urea, Triton acetic acid-urea or with ampholines conditions can be run on horizontal platforms.

You have to separate the cathode and anode chamber, and that is certainly easier to achieve, if you have a apparatus built to run vertically.

has to do with convience too. imagine making a SDS-PAGE gel with two layers horizontally!!?!?!

Just convenient to pour and run ! If you had a horizontal apparatus that worked easily I am sure we would have it by now :)