Term to describe when one event cannot occur without the other

Solution 1:

Catch-22

To use it in a sentence, "It's a catch-22" or "It's a catch-22 situation"

From Google's definition of Catch-22:

a dilemma or difficult circumstance from which there is no escape because of mutually conflicting or dependent conditions. "a catch-22 situation"

(Paraphrased very slightly) from Wikipedia's Catch-22 (logic):

A catch-22 is a paradoxical situation from which an individual cannot escape because of contradictory rules.

An example would be:

It's a catch-22 situation: To apply for a job, you need to have a few years of experience. But in order to gain experience, you need to get a job first.

Origin is from the book, Catch-22 by Joseph Heller.
From the Wikipedia page for Catch-22 (book):

The phrase "Catch-22" has since entered the English language, referring to a type of unsolvable logic puzzle sometimes called a double bind.

From the Wikipedia page for Double Bind:

A double bind is an emotionally distressing dilemma in communication in which an individual (or group) receives two or more conflicting messages, and one message negates the other. This creates a situation in which a successful response to one message results in a failed response to the other (and vice versa), so that the person will automatically be wrong regardless of response. The double bind occurs when the person cannot confront the inherent dilemma, and therefore can neither resolve it nor opt out of the situation.

Solution 2:

This sounds like a chicken and egg situation.

a situation in which it is impossible to say which of two things existed first and which caused the other It's a chicken and egg situation - I don't know whether I was bad at the sciences because I wasn't interested in them or not interested in them and therefore not good at them.

Cambridge Idioms Dictionary, found at thefreedictionary.com