The main thing is that paper gives you a sense of control that a phone takes away. When you write by hand, it's your personal space - no algorithms are tracking what thoughts you're writing down or suggesting alternatives to your diary. An app can close at any moment due to an update, sync to the cloud, disappear if the company shuts down the service. But a notebook - it's just sitting there in your desk, and it's always yours.
There's also a physical aspect that people often overlook. When you write by hand, you can't write at the speed of thought - you have to slow down, rephrase, find the right words. This isn't a drawback, it's actually the point: you get a better grasp of your feelings because you're not just dumping a stream of consciousness, you're living through each sentence. In an app, it's easy to churn out a wall of text that you won't even want to reread later. Plus, on paper you can see how your handwriting changes depending on your mood - that adds another layer of information about what state you were in.
And the last thing - it's about memory. When you write in a notebook, you develop a habit, a ritual. You remember what you wrote on the left page three weeks ago because you remember how you were holding the pen, how you were sitting. In an app everything blends together, everything's in the same font, the same interface. It's harder for your brain to anchor it, and the entries don't stick in your memory as well.