Why are we not supposed to heat Erlenmyer flasks?

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This really depends on what you mean by heating.

One of the main uses for Erlenmeyer flasks is for recrystallization, which of course involves heating the container and contents. Typically this is only moderate heating, such as over a steam bath or with a hair dryer. Some manufacturers specify that their Erlenmeyer flasks are ideal for heating applications.

Traditionally, boiling flasks have more uniform and thicker walls, which allow for much greater heating limits, and a more uniform heating distribution. They are designed to handle more intense localised heating, and manage thermal and physical shock distribution. Erlenmeyer flasks usually have thinner walls and greater wall thickness variation, and are less able to handle sudden thermal changes, such as heating with a high energy source like a Bunsen, or heat gun. Using them in this way may well lead to cracking, fracturing or worse, and is unsafe.

So, although Erlenmeyer flasks can be heated, they are not specifically designed for high temperature, constant heating applications. For this, you should use a boiling flask.