What makes a photo 'beautiful'? What makes a design 'good'?

This is not (just) about taste. This is about criteria, and what is important to the audience.

With photos you can look at specific photographic features, such as sharpness, use of color and composition. For example, the eyes in a portrait photo almost always have to be sharp, that is what attracts the most attention. However, it can also be a (artistic) choice to put the focus somewhere else or to have nothing in focus.

Portrait with the focus not on the eyes.

In addition to checking photographic features, you can reflect on the emotional response a photo invokes. Some photos are intended to be disturbing, and this emotion adds to the 'beauty' of the photo.

What is happening here?

So when critiquing a photo, you can talk about the photographic features and how these contribute to (or distract from) what the photo is trying to tell. And you can talk about the emotional response you get from it.

Similarly, when critiquing a design, you can talk about the design features (e.g. alignment, color consistency, use of white space, balance in font sizes). And you can talk about the experience (emotional response!) it should invoke with the audience.

And whether you are critiquing a photo or a design, keep it factual, constructive and fair. You can be honest and friendly at the same time! This is how teams and people can learn and improve, and be motivated to do so.