The argument comes both from the fact that Jesus was fully human, and from the Hebrews 4:15, which says (in the King James)
For we have not an high priest which cannot be touched with the
feeling of our infirmities; but was in all points tempted like as we
are, yet without sin.
This outlines the fact that even though Jesus is fully God, He was also fully human. He felt all our infirmities and weaknesses, and yet, as God overcame them.
A complete theological statement would be "because Jesus was fully Human, He had the capacity to sin, but because of His perfect nature, also being fully God and therefore perfectly good, He could not sin."
Both are true, but people have a hard time wrapping their head around that, choose half the truth, and fall into error.