I am trying to recreate this sphere with webbing on it in Illustrator. I tried a lot of things but I can't get the same outcome. I think I am overthinking it but I can't seem to figure it out. Could someone point me in the right direction or tools to do this?
As it looks like a 3d effect, let's apply that effect.
Make your logo a Symbol. We will use it later.
Draw a circle and cut it half. It will be used to make a ball.
Select the semi-circle and go to Menu>>Effect>>3D>>Revolve.
Use the setting of the attached image...
Click the Map Art... button and load the symbol.
With some more tweaking, you can get the desired look.
See the image below for values used: