Why it is a bad practice to use break/continue labels in OOP (e.g. Java, C#)?

break and continue are not functional style programming. There is nothing about OOP which suggestsbreak, continue or even goto within a method is a bad idea.

IMHO using break and continue are discouraged in OOP languages as they can lead to complexity and confusion. As Labels are used rarely they can confuse even further. I would say you should still use them when you feel its the simplest solution to the problem.

// confusing use of LABEL
http://www.google.com/
do {
    if (condition) continue http;
} while(condition2)

another confusing use

GOTO: {
    // code
    if (condition)
         break GOTO; // without a loop
    // code
}

Good use of a label

OUTER: 
for(outer loop) {
   for(inner loop)
      if (condition)
         continue or break OUTER;
}

Odd use of a label

FOUND: {
   for(loop)
      if(found)
          break FOUND;

   // not found
   handle not found
}

The person who told you that would probably means that break and continue are branching statements like goto which are one mechanism of imperative programming.

A break/continue only allow you to jump to an outer statement, which means that you cannot go everywhere in the code. So you stay in the same method object, so it's not incompatible with OOP.

Anyway, saying that break and continue are not OOP is a non-sense. We can discuss about their impact on the readibility maybe but that's all.

The advice not to use break/continue is probably not really related to OOP. It is based on the fact that these statements are similar to the infamous GOTO, which can make code completely unreadable. However, dogmas are bad counsels. The main paradigm should be readability of the code. Jumping out of a loop in the first line using break or continue can be much clearer than putting the whole rest into an if condition.