I would say the key is to see that T bonds to A (as shown below). There is nowhere for a 3rd hydrogen bond to form, unlike between C & G. Orientation and polarity must match up for hydrogen bonds. The C-H bond (shown below as the bottom left corner of the 6C ring on adenine) on Adenine can't participate in hydrogen bonding since it isn't polar.
The C-G bonds are setup perfectly for 3 hydrogen bonds as depicted below.
At least that's my take on it.