Fluctuation in pH reading on pH meter
Your teacher gave you a poor answer.

You are observing three different things. 

(1) The solution isn't instantly homogeneous when HCl is added. It takes a couple of seconds of stirring to mix it thoroughly. 

(2) The calcium hydroxide solution initially has considerable buffer capacity. As the solution gets less basic then a small amount of HCl can change the pH by a relatively large amount. So a drop of HCl in 50 ml of 0.1 molar calcium hydroxide won't change the pH much, but a drop of HCl in a  neutral solution at pH 7 would change the pH by quite a bit. 

(3) The electrode and meter have a response time. So if you could move the pH electrode instantly from an acid solution to a basic solution it would take the electrode and meter themselves a few seconds to equilibrate. (The pH electrode has a hydrated silica layer that forms the boundary on the surface which takes time to equilibrate. The pH meter itself will have some RC time constant so that electrical noise is minimized.)