Note how plurals of «соба́ка» and «ко́шка» end in И: соба́ки, ко́шки, even though you might expect А to turn into Ы.
There are some restrictions on which consonants are used with which vowels when making word forms. Here are the rules for и, а, у vs. ы, я, ю:
К, Г, Х are called velar consonants (i.e. made in the back) and Ш, Щ, Ж, Ч are often called hushes. The latter do not show palatalized/non-palatalized pairs in modern Russian, so the spelling rule does not affect pronunciation anyhow. It's just a convention.
It is not too important for you at the moment, but you may notice how О and Е sometimes appear in consonant clusters or disappear from them. For example:
Later you will encounter the Genitive plural (often used with numbers and words like "many" or "few"), which shows a simple pattern for -к-suffixed feminine nouns that do not have a vowel before "-ка":
As you can see, the vowel (О or Е) depends on whether the previous consonant is palatalized or not. Hushes behave as if they were palatalzed, despite Ж and Ш having lost this quality in the modern language.