How can I make a latch in AVR without interrupts?
Your problem might be bouncing. When you press or release a button, it bounces. (see picture). This is due to mechanical bounces of the electrical contacts inside the button itself.


You have to take this into account and reject the bounces. This can be done in software. A lot of method exists, using timer, interrupts, wait loops etc. Google the web and choose the implementation that fits your system best. 

You can also have a look here: debouncing-buttons