Those hand sanitizer pumps that you have at work contain a hand sanitizer solution that contains alcohol as the primary anti bacterial agent. This form of hand sanitizing agent is used in most hospitals around the world now, and dozens of studies have shown that they are very effective at killing bacteria and preventing the spread of infections. They are also very safe and easy to use!
Your friend at work is wrong. Although it is true that bacterial resistance to various chemicals and antibiotics is a problem in some settings, alcohol is a substance that is very potent and kills bacteria directly by coagulating their proteins. Since this is a physical mechanism for direct bacterial killing (rather than the typical biochemical mechanisms that antibiotics use) there is no possible way for bacteria to develop resistance to alcohol. Therefore, using these alcohol based handrubs will not in any way contribute to making the bacteria stronger.
The fact that these hand sanitizers are being used outside of the hospital, in offices, restaurants, and other public locations, is excellent, because it is an easier method than washing hands and will contribute to better hygiene!
As always, you should ask your primary care doctor
regarding general health questions like this one.