Comma After That Is Why

That is why looks like a conjunctive adverb or an introductory phrase that must always be followed by a comma, but it is not.

Here is the full list of conjunctive adverbs provided by the YourDictionary online reference:

Conjunctive Adverbs

accordingly

additionally

also

anyway

besides

certainly

comparatively

consequently

conversely

elsewhere

equally

finally

further

furthermore

hence

henceforth

however

in addition

in comparison

in contrast

incidentally

indeed

instead

likewise

meanwhile

moreover

namely

nevertheless

next

nonetheless

now

otherwise

rather

similarly

still

subsequently

then

thereafter

therefore

thus

undoubtedly

yet