# What is the intuitive meaning of these statements in the context Bayesian prior and posterior?

I am now familiar with the Bayesian thinking process of using a prior and then getting the posterior once we observe data using the prior.

I read the following statements which I am trying to get my intuition but unable so far. Any intuitive explanation will help.

A conjugate prior may always not lead to a better MAP estimate. Also, it is not clear what is a "better" MAP estimate

Why does a conjugate prior always not lead to a better MAP? I thought if you have a conjugate prior it is always easy to maximise the posterior integral.

Another downside of a choosing a conjugate distribution for the prior is that for some problems the conjugate may be inadequate.

In the above context what does inadequate actually mean?

Thanks a lot. Much appreciated.