The falling action is everything that comes after the part of him crying at the milk bar and feeling guilty. Basically everything after the line, "When the crying spell passed, he wiped his eyes and face with his hankerchief, feeling relieved."
If I understand correctly, you’re asking why “I have a lot of great skills that would really help your company be successful” is ineffective. If that’s correct, it is because he does not list or name any of this skills therefore, the statement is ineffective.
Money is at the heart of the conflict.
Explanation:
Eliza (the girl) was insisting to pay for her lessons even though Higgins did not demand it. It was due to the hesitation of Higgins to teach her to speak gently. Eliza deciphered this as Higgins reluctance of not working for free since he must have thought that poor flower girl won’t have enough to pay for his speaking course.
To clear the air regarding the same, Eliza kept insisting for following a professional approach where she would pay for her speaking course.