cough so Matthew is my favourite character in the series. He has been my main unit from the release of the game. So obviously I have probably poured in more into him than anyone else would be willing to do.
My friends told me to share my experience with him, so I'll try my best!
That said, most of his weaknesses have already been mentioned here. General rogue problems, low resistance, non existent damage with his standard dagger.
So instead I'm going to focus on what he does, in my experience, do incredibly well.
So first off, as said in comments before me, killing hard and fast is what you need to do in this game, and unfortunately unless you give Matthew a poison dagger, he will do none of these things. But when you do invest those 20000 feathers in upgrading a kagero, you're probably going to wonder "why wouldn't I use kagero?" In my experience matthew's higher hp, defence and speed makes him much more survivable and therefore a longer threat in the game. Now his atk is much lower than her, so he won't have that immediate "oh fuck" you have when meeting a kagero (as any infantry unit). Unfortunately my first matthew happened to be +hp -atk. So what I've come to realise is that it's all about finding those damage thresholds, after all you don't need to overkill, just kill, right? +atk for matthew is basically essential. Then he only gets better the more you manage to buff his attack.
Where he truly shines is if you are willing to give him close counter. With his decent speed and defence he kills almost every melee infantry and archer in the game (yes, even cordelias on steroids, if you give him a rally defence). By adding vantage to his kit, he can survive a counter and kill all units on the 2nd turn. In my experience he survives mages well enough that he either one shots them or kills on the counter.
To me what makes matthew worth the effort is his flexibility in being a lethal colourless that can survive a hit or two makes him really good in a lot of modes.
Now, does he suffer in the current cavalry heavy meta? Absolutely :"D. But invest in him and he'll be a very rewarding unit to use in modes like tempest trials, voting gauntlet etc. And against infantry teams during the arena assault ^
Thank you for your time! And sorry for the rough format.