Here's why:
* Present participles end in "-ing" and function as adjectives or adverbs. They describe an action that is happening or ongoing.
* Infinitives are the base form of a verb preceded by "to" (e.g., "to rely").
In the sentence "He is relying on his instincts," "relying" acts as the present participle of the verb "rely" and describes the ongoing action of "relying."