Is it the sphincter that flexes when a human pushes a bowel movement? Of course the sphincter muscle is at the exit point. To use a toothpaste tube analogy, if I want to squeeze out some toothpaste, it does me little to no good to jostle the nozzle; I need to squeeze the tube (which is analogous to the colon) to get the paste (payload) to come out. So when a human is sitting on the toilet squeezing, is that squeezing flexing of the sphincter, or squeezing muscles along the sides of the colon pushing on it as one's fingers push on the tube to get toothpaste to come out. If it's the sphincter that's getting flexed, how is that helping get a big log out?

The pressure that you apply when you push during a bowel movement derives from an increase in the pressure of the abdomino-pelvic cavity. You generate this pressure by closing the glottis (the opening to the lungs) and contracting the anteriolateral abdominal muscles (i.e., the external oblique, internal oblique, and transversus abdominus). This reduces the volume of the (now sealed) abdominopelvic cavity and increases pressure helping to drive feces from the rectum. This is mechanism is also used to expel urine and during childbirth.

If you do this with the glottis open, then you forcibly exhale because the increased pressure of the abdominopelvic cavity is transferred across the diaphragm and into the thoracic cavity compressing the lungs.