Learn Dutch: Er moet een theorie zijn die dit patroon uitlegt. - There must be a theory that explains this pattern.

No, here moet is used for logical deduction. Just like in English, it means you are making a strong assumption based on evidence. You are concluding that it is highly logical for a theory to exist, rather than expressing a strict obligation.

Why do we start the sentence with Er?

Er translates to 'There' in this context. Just like in English, Dutch uses it as a placeholder subject when introducing something new and indefinite (like een theorie) alongside the verb zijn (to be). You generally cannot just say 'Een theorie moet zijn'.

Why is the word die used here for 'that' instead of dat?

The word die refers back to een theorie. Because theorie is a de word (de theorie), we must use die. If we were referring back to a het word, we would use dat instead.

Why is it dit patroon and not deze patroon?

Because patroon is a het word (het patroon). When pointing something out, you use dit for singular het words, and deze for singular de words as well as all plural words.