(Totally guessing at the flair.)
There are a couple reasons! The main one, though, and probably the most impactful, is that crying changes the size of the throat muscles that control your voice (larynx), making your vocal pitch and tone change.
As a singer, I can address this! When you cry some of the tears run through your mucus membranes. They swell, when one mucus membrane swells they all do. Additionally, the tears mix with mucus and drip down your nose (why your nose runs when you cry). Some also goes down your throat. This causes even more vocal fold swelling.
Sinuses get clogged, breathing quickens, and lips tremble affecting the pitch, tone, and timbre
The purpose of crying is to signal distress so your body overrides your will like it does when you try to stop breathing.