The biggest issue for Access databases is that if you keep the whole package in Access (as opposed to Access front-end, something else for back-end data), you run into a few simple but serious problems.
1. Access uses your network as a FILE SERVER, which means if you run a big, whompin' query, you have transfer a LOT of data over the network. That is, the query is processing remotely-held data on YOUR machine. For small recordsets, this is not a problem. For big recordsets, you churn your network hellishly.
If you have split the database into an Access front end and a something-else back end, the query gets run at the server, not on the client (your workstation), so the record transfer is only the solution set for your query, not the whole raw recordset.
2. Access security isn't as robust as security for other systems. The granularity is limited because Access was designed as a small-system relational database manager. One of the central tenets of security is "Know your users." For the size of database suggested by Access, that is possible. For larger user bases, it is not.
By switching to a more robust back end solution, security can be better maintained and/or defined.
3. Access data safety features are not consistently present. In specific, you have to design your own record-level data auditing methods. I.e. if you want an analytic report of every change made to your database, you are going to write that yourself. There is no change-history auditing for standard Access.
By switching to a back end solution that supports field-level change records (audit records), you can over come this problem.
4. Access uses VBA for its code, which isn't necessarily what all IT professionals use. Many like Ada, "pure" SQL, or some C++ variant for direct compilation. Or they use J++, Javascripts, etc. VBA is powerful and pretty much a high-capability language, but it is just not the most popular of all languages among the world of computer programming.
Back end solutions that have more than one data interfacing method can overcome the Access VBA problem.
5. Access has limitations on record sizes, numbers of elements, and a few other structural constraints that some folks don't like - even though most Access databases rarely reach the limits. Some designers just don't like designing in a low-limit environment. Nor can I blame them.
Most of the more robust back end solutions have either no limits in theory or have higher limits than Access. Longer records, more records, more complex joins, more versatile indexes, etc.
Despite all these limitations, there are times when Access is still the best choice for doing some data management tasks. Thinking 'small' is not always bad when the problem is also quite 'small' - but IT professionsal often think big.
In summary, those who don't like Access have good reasons when the database in question is big enough or complex enough to trigger their fears. In that case it would be up to you to assure that they understand WHY Access is still the best choice. If you can't come up with more than just a couple of good but very minor reasons, the odds are that Access ISN'T the best choice in the first place.