A Banshee rush can be extremely annoying and cause you to lose focus on build and fall behind in the macro game. This will almost assuredly lead to a loss later in the game. To prevent this, try out this build order to get counter a Banshee rush and stop worrying about early pressure.
Banshees are light air units that can only attack ground. They do a huge amount of damage though, taking out Marines and SCVs in just 2 shots. One of the best counters that Terran has to a Banshee rush is getting an early Thor out. Thors do a lot of damage to light air units and can take out a Banshee in 3 shots. Plus if you get out your Thor as fast as you can, it will come out around the same time your opponents Banshee does.
If the Terran player researches Cloak you’ll be in for another problem though. Your Thor won’t be able to shoot what it can’t see. To solve this as soon as you know that he’s going to Banshee rush you, stop calling down MULEs from your Command Center. Save up all your energy to scan where the Banshee is so you can shoot it down.
Another option you have is to build an Engineering Bay then put one Missile Turret in your mineral line to protect your economy. Missile Turrets can reveal cloaked units at a longer distance than they can shoot, so if you have one near your Command Center a nearby Thor will be able to help take out a cloaked Banshee no problem.
There are two deadly things that you must steer clear of if you want to effectively counter a Banshee rush. Going overboard with static defenses is the first. If you build a lot of Missile Turrets then you’ve wasted a lot of minerals that you could have spent on units or an expansion.
The worst thing you can do when getting Banshee rushed is to let it affect your macro play. If you get distracted and forget to make SCVs or expand, you’ll fall behind in economy and end up losing the game later on.