I create a lower pressure and the higher atmospheric pressure pushes the liquid through the straw.
If the air around the drink was at half the usual atmospheric pressure, then simply sucking at 3/4 atmospheric pressure would not draw liquid into the straw. To the contrary, it would push air through the straw the other way.
Not if the straw is too long, it can't. In fact, that was how atmospheric pressure was first demonstrated by Torricelli (the word torr for pressure is from his name).
If you take a column of water that is enclosed at the top, opens at the bottom into a source of water, and is over 34 feet tall, the water will NOT stay at the top. It will drop and create a vacuum at the top of the tube. The level of the water will drop to be about 34 feet. No amount of suction can make it go higher.
That height of water represents the weight of the atmosphere pushing down at the water at the bottom and making the water level rise.
By the way, the reason we use mercury for barometers is that it is much more dense than water and so is not pushed up nearly as high. You could make a water barometer (Torricelli did) but it would be 34 feet tall.
You might want to learn a bit about atmospheric pressure.
Evangelista Torricelli - Wikipedia
Barometer - Wikipedia