Why do people love running down mid when they have a slight advantage

Hi my names Kyovulpes and I'm pretty new to the game. Well as in to say this is my first year playing, climbing, all that junk, and I'm learning how to improve my game play macro wise as a Adc main. Now last game I just had ass twitch the game kinda stall out to be pretty long. We took the mid inhib tower and one of my team mates wanted to just run it down mid to try to take the inhib. Our comp wasn't a siege per say we were more like a pick team you know? I said that pushing mid to get 1 inhib where a fight WILL happen is kind of a...bad idea. I offered that we split and take the other inhib towers since that would give us more pressure and more room to fight. My main question is what would you have done as me in that situtation. Should we as a team run it down mid and try for the inhib and risk a possible throw or I am I sorta thinking the right way? I need like some great ideas and convincing arguments cause when I climb after the season starts I wanna want the best possible out come to secure the win. I put the match in there I was the twitch so yeah did I do ok? could I have done better? mind you Im still learning I don't mind criticism at this point. Thanks.