When they say "Access" many people really mean "Jet/ACE", i.e. the data file sharing mechanism of MDB/ACCDB files. Jet originates from the days when SQL DBMSs were big, expensive and complex. Jet and like products provided a cheap desktop alternative to a SQL DBMS. That segment has largely vanished, mainly because the market-leading DBMSs now come in versions that are cheaper (usually "free"), extremely easy to install/maintain and provide a far wider range of features out of the box than Jet/ACE ever will. Jet/ACE will probably be around for years but if it ever was going away that would be no bad thing for Access because Access is a much more powerful tool when used with another DBMS than it is with Jet/Ace.
On the other hand, Access as a development platform is a perfectly fine tool if it suits your development needs. It's always going to be a niche product compared to the leading application development platforms. Some of Access's features are dated and have suffered long-term neglect by Microsoft for whom the product isn't a high priority. Access still does many things you would really struggle to do in Excel.
For reasons of security and supportability many IT departments actually don't allow Access applications on production servers. Perhaps your colleague is referring only to the policy at your organization rather than making a general comment on the product itself.