This final step is more easily said than done. The entire volume is based on the first few lectures. After a few examples and some further discussion, the fog may tend to lift a trifle. In my opinion, qualitative discussions enhance quantitative discussions, but are not a substitute for them. The physics is in the calculation, not in the words which can be used to describe the result.
Words can be part of a proof, but are more often a mnemonic for the real arguments.
For many years the oft-quoted explanation, if analyzed, actually proved the wrong result. The objective of science is to explain all physical phenomena in a consistent axiomatic way. Correct natural laws are always correct. Momentum conservation cannot be suspended just because it is convenient to do so. Approximations have mathematical limits on their validity, and can only be used consistently within those limits.