Did you read the description of the apparatus? Did you read how the two beams of light are sent into two arms at right angles (not in opposite directions, as you said)?
Did you read how the experiment was done, not just at different times of the day (so that the apparatus would be moving in different directions due to the Earth's rotation), but at different times of the year (so that the apparatus would be moving in different directions due to the Earth's motion around the Sun)? Did you read how the whole idea of the experiment was to detect the Earth's motion, not relative to any light source, but relative to a hypothesized medium through which light traveled, the ether? And how the null result of the experiment cast doubt on the whole hypothesis that there was such a medium at all?
If you run a similar experiment with sound, you will find, as others have pointed out, that the velocity of the observer relative to the medium--air--affects the speed of the sound waves that are observed. The velocity of the source does not come into play. By analogy with this, it was expected that the velocity of the Earth (and therefore the M-M apparatus) relative to the ether would affect the speed of light that was observed in the M-M experiment. But it didn't. That shows that light does not work the same as sound in this respect--which was not the result that M&M originally expected to find. More importantly for this discussion, the null result of the M-M experiment shows why the explanations of observed speed that work for sound won't work for light.