Why should a thermometer not touch the sides of the beaker while measuring the boiling point of water?

Because then you would not actually be getting the temperature of water you would be getting a reading of the temperature of the side of the beaker. So if the thermometer is surrounded by 100% water then you will get an accurate reading, but if it touches the side of the beaker then that will affect the temperature and make it lower than the actual boiling point.