‘You can’t teach an old dog new tricks’ means, something that you say that is difficult to make someone change the way they do something when they have been doing it the same way for a long time. This can be for example;
“You can’t teach an old dog new tricks. You’re never going to change him, he’s been doing it that way for 30 years“.
Even if it would seem that a better system has been developed. Generally, we humans do not like change!? Also, see below.
‘If it’s not broken why try to fix it’, also said in another way; ‘If it ain’t broke (isn’t), don’t (or why) fix it’ means, that some people will say it is a mistake to try to improve something that has been proven over the years.
Example; “What’s wrong with the way we’ve been doing it since I started work here? If it ain’t broken why fix it?”
However, sometimes things do need to be improved. An example of this can be at work where systems or routines have been in existence for many years and then suddenly the management want to change the process, possibly to modernize and improve. But some people are ‘stayed’ in their ways and do not like change.
‘Stayed’ means, to remain in the same position or same condition. Not moving forward. You could say that some people from the older generation will not, or do not want to ‘move forward’ or learn something new. Even if it is for the better! As said above. We don’t like change.