Condo Kitchen Sink Backup

Tenant reported a kitchen sink backup incident in July.  The building maintenance came to rod the sink and clean the dirty water.  Last week, the same incident happened again.  The building did the rod again.  The backup damaged the laminate floor and drywall.  I filed a claim with my insurance company.  The insurance company wanted to know where the blockage located to determine coverage.  Our HOA property manager said the cause of the backup is unknown but the clog is at the branch line at my unit.

Anyone has experienced this before?  What is the cause of the kitchen sink backup?  How to fix this (it happened twice in 3 months).  The 2nd time when this happened, my next door neighbor unit had the kitchen sink backup too.  The building said it was because of the blockage on my side.

I am confused if it is my branch line got clogged, why that affected the neighbor's kitchen sink (sounds to me it was the main line that got clogged).  If it is my branch line, I am wondering what the tenant did to make it clog twice in such short period of time. 

Tenant want to break the lease and move out.  She still has 7 months of lease left.  Every time when this happened, the building staff came right away to work and clean the unit.  But tenant said the unit is not livable because she does not know when this will happen again. 

Can anyone please give me some idea on what might be the issue, how to fix this?  And also does tenant have the good reason to break the lease? 

Thanks in advice for any input!