Extending lease by a month then rescinding

Hi everyone -

I had a two-year term that was ending on July 1st - towards the end of April the agency reached out and ask if I wanted to extend my lease. I said I was planning on moving out but asked if I could extend it to August (this was via email).

My circumstances to change and I actually do need to move out in July so on May 14, I asked if I could bring forward the lease and date to July 15 instead. They said no because the period had ended.

What grounds do they have to keep me to August 1? My lease states July 1 and I never signed a formal extension. It was all just email correspondence.