<p>I have no idea what context this remark was made in. The statement that he made hasn’t a list to correct for parallelism.</p>
<p>In general, I can explain the rule. Gerunds are verbs in their “-ing” forms. When you add an “-ing” to a verb, it becomes a noun, e.g.: </p>
<p>(1) I like to run because it is fun.
(2) Running is fun. </p>
<p>In the first sentence, “to run” is an infinitive-- it is the non-conjugated form of the verb. In the second, “running” is a noun, and its action is a state of being; “is” is a verb operating on the gerund. </p>
<p>Whether in an infinitive form or not, verbs cannot be combined with nouns in a single list. Verbs can’t even be combined if they aren’t all in the same conjugate form. (Although it’d be doubly wrong to make a list with a conjugated verb and a gerund, or an infinitive, but that’s beside the point.) </p>
<p>An example:</p>
<p>I like to run, dancing, and to play soccer.</p>
<p>Obviously this is wrong. You can correct it in one of two ways:</p>
<p>(1) I like to run, to dance, and to play soccer.
(2) I like running, dancing, and playing soccer. </p>
<p>Here we have corrected for parallelism; i.e., we have made it so that each element of the list is in the same form, whether infinitive or gerund.</p>