I've asked several other questions like this, and I know it's a dumb question but I really can't understand. When light is emitted from a moving source, it still moves straight in that source's frame. I understand that the path can look different in a different frame, but taking a pond of water as an analogy to the E&M field, I don't understand why a moving source would see emitted light in their frame as still moving straight. Perhaps it's a misunderstanding of the E&M field, I just can only think of some person running parallel to some water, and tapping the water as they run. The disturbances won't move with them, they'd stay behind. Does this mean that when objects move, they pull the E&M field with them? How much would be pulled? Clearly I'm just not understanding something very obvious, but I can't figure it out. I'm sorry for all the reposts.
When it comes to light any analogy with water is doomed to be completely wrong.
I word this so strongly because it is a common misconception that frustrated all of physics for several decades back around the turn of the 20th century. People kept trying to make analogies with water, and the result was always wrong.
What you are describing is what is known as the aether theory of light. People thought "well, light is a wave, and water waves need a medium to travel through, therefore there must be some sort of medium in which light travels." This is simply not true. The EM field is not some sort of physical substance that has a bulk velocity. When light is emitted, it is not perturbing some medium that is stationary in some reference frame. It propagates, and you can describe that propagation in any frame you like, but there is no "correct" or "natural" frame.
Michelson and Morley are most famous for designing the experiment that proves this beyond any reasonable doubt. Basically, they measured the speed of light in various directions, aligned with and perpendicular to the Earth's motion about the Sun. That speed did not change, not one bit. The Sun's rest frame is nothing special; the source may be moving with respect to it, but so what? Light moves away from its source, at the speed of light, in a "straight line," as seen by any inertial observer.
If you thought otherwise, you would have to believe that some inertial frames are more important than others; that some observers/sources are really, truly, absolutely in motion while others are truly at rest; that the shore of the pond was a more privileged thing in the universe than person running alongside it. Physicists eventually realized this was preposterous - the universe doesn't think the shore of the pond is more special than a person - and hence was born special relativity.