Why do Japanese anime characters shout so much?
First off, welcome to Anime &amp; Manga!

Suddenly shouting is a trope used in a lot of media, not just anime &amp; manga.

It is often used in the following scenarios:


In anger: When a character reacts to a situation with rage, much like in real life, shouting can be expected to follow.
In fear or surprise: Again similarly to real life, when taken by surprise, people often exclaim loudly almost reflexively.
For dramatic effect: More often seen in media, when an important event or statement requires additional attention, it is often shouted to give it just that.


The conversation above in particular is likely for dramatic effect - I couldn't say for sure as I don't know the context of the whole show.

See this page for more information.

Also related is this question. Shouting the names of attacks naturally fits into the third option.