So, first of all, the sentence （私は）月曜日にいつも兄と一緒に食べます。 is grammatically totally fine and would be comprehended in the context you give. This would probably best structurally translate as

"I usually/always eat with my brother on Mondays"

However, partly because Japanese is a pronoun-drop language, and partly because of the situation -- where the speaker has been asked about going for pizza (presumably on a Monday) -- 月曜日はいつも兄と一緒に食べます might well be preferable here.

The reason for that is that he's focusing on the concept of Monday, so it makes sense to make it the topic/discourse of the conversation. In comparison to the above sentence, you'll thus get a structural translation of something closer to

"On Mondays, I usually/always eat with my brother".

Using は thus makes it a bit clearer that its the pizza invitation being on a Monday that is the issue with why he can't go, which is appropriate for this context.

Hope that helps.

So, first of all, the sentence （私は）月曜日にいつも兄と一緒に食べます。 is grammatically totally fine and would be comprehended in the context you give. This would probably best structurally translate as

"I usually/always eat with my brother on Mondays"

However, partly because Japanese is a pronoun-drop language, and partly because of the situation -- where the speaker has been asked about going for pizza (presumably on a Monday) -- 月曜日はいつも兄と一緒に食べます might well be preferable here.

The reason for that is that he's focusing on the concept of Monday, so it makes sense to make it the topic/discourse of the conversation. In comparison to the above sentence, you'll thus get a structural translation of something closer to

"On Mondays, I usually/always eat with my brother".

Using は thus makes it a bit clearer that it's the pizza invitation being on a Monday that is the issue as to why he can't go, which is appropriate for this context.

Hope that helps.