Very late, like years late, but I gotta answer this. It'll be quite long, so skip to conclusion at last paragraph if you are familiar with every episodes from SG-1 and SG:A, mainly ones cross-referencing each other.
That whole thing is because of how the macro works.
Pegasus gate always supersedes Milky way gates. This is a fact stated by Dr.McKay. We star here.
When there is two gates near each other, whatever you do, in normal gate operation, Pegasus gate activates first when you dial in from whatever location. That happens when Wraith attacked Earth at .
Midway station is at the farthest distant possible from each galaxy. you could gate midway from each galaxy without ZPM, if you are at the outer plant of the galaxy. That is verified when they used Daedalus as relay point to send message to each other to warn about Trust, also when Teal'c relayed message to Atlantis and to SG-1 when they tried to open gate to Milky way supergate from Pegasus. They only use the Mckay-Carter macro because they want to gate from Atlantis/Earth gates. Only, it is confirmed that Atlantis can gate Midway without any problem, possibly because Pegasus gate has better power consumption rate or so. Still, Earth gate cannot do that.
The macro works like this. When they open the gate to midway using macro, they actually open the gate to next gate of the series, then stores it in buffer, open next gate, sends, and do on.
However, like I said, Pegasus gates always supersedes Milky way gates.
So, if you think about this, There is a big danger using Pegasus gate and Milky way gate in mix, as we know how dangerous to play with buffer. There was one time when Teal'c was stored in buffer and gate shut down before he could be re-materialized on Earth-side. They mentioned that buffer could be erased if they open any warmhole while anything is stored.
So, think of it this way. Imagine there is no Midway station. You opened a gate to Atlantis form Earth using macro. That actually means you opened a gate to next gate in series. Gate sends it to next gate, next, next, and so on, and voila, you are in Atlantis.
Now, it's same situation. No Midway. Earth is sending people to Atlantis using macro. Now, buffer is sent to next gate in series, and so on. However, this time, Atlantis gates to Earth at exactly same time as Earth. So, each traveler's buffer meets where Pegasus-Milky way gate meets. there's no Midway, so they will be farthest distance. Now, two gates are storing buffer, and try to gate each other. As we know, Pegasus gate supersedes Milky way gate, and opens warmhole first, ignoring dial from Milky way gate. Then, buffer stored in that gate is erased and accept one from Pegasus. So, traveler from Earth is "erased".
It is simple as this. you cannot know when Milky way or Pegasus will dial each other. Because macro actually opens gate to next gate in series, they don't know if gate at the other end of macro is opened or opening. Pegasus gates "always supersedes" Milky way. So, if when they dial each other at the same time, buffer meets at the middle, Pegasus gate supersedes Milky way one, opens warhole and delete buffer from Milky way and stores one from Pegasus, deleting traveler from Earth while.
So, Midway station is to let travelers from Earth to safely stand while Pegasus travelers come in from Atlantis. Dr.Mckay had to tweak the gate system so Milky way macro actually open warmhole to Milky way gate, which is the whole point of Midway station. As long as Milky way gate only gates to Milky way gate, making Pegasus gate invalid, having two gate at the same point in space has no problem. Pegasus gate will supersede, which means Pegasus macro will gate to Pegasus gate, while Milky way macro invalids Pegasus gate and open warhole to Milky way gate.
Yep. That's the whole point to have Midway station. Because of the Macro, and how the gate system works. It's actually a workaround to the problem. But then, it found it's usage as 24h quarantine.