We use writing and speaking for the same purpose- to communicate. Although speaking comes to us naturally, we learn it almost instinctively but writing has to be taught to us and it may take several years before we learn to write properly.
In the olden times, writing was considered more prestigious as only some people knew how to write. But now almost everyone can read and write.
However, we still have no idea what is more important?- speaking or writing?
Let’s look at it in detail!
It's just faster this way
The good thing about speaking is that you can get feedback very quickly. You can also clarify your doubts at the same and ask any questions that you may have!
The same cannot be said about writing as you don’t know when you’ll get the reply, or are you even getting one or not!
Also if you want to convey anything, speaking is a lot faster than writing. Just imagine how much time it would take for you to speak 5 sentences and to write 5 sentences.

It's 'WHOM', not 'WHO'
Speaking contains lots and lots of grammatical errors. Sometimes we don’t even make full sentences! It is full of repetitions and false starts and hesitation.
However, when we write we suddenly become very proper and it is usually grammatically accurate.
This is because when we are speaking, we don’t get enough time to make any corrections to what we are saying but when we are writing, it gives us ample time to make our writing very grammatically correct.

A long time ago!
The good thing about writing? It’s durability! Some scientists are still researching what a certain someone wrote some thousands of years ago.
Durable right!
But since there was no equipment to record yourself in the olden times, speaking isn’t really durable. However, now we do have the technology we can also preserve what we are speaking!

Social Cues!
When we are speaking, we generally use more than our mouth. We may nod to show our approval, shake our head for disapproval, use hand gestures a lot. Basically, our body language also comes into use when we are speaking.
However, the same cannot be said about writing. Hell, no one can even see our facial expressions!

Now, you can't take that back
Now, you can’t take back things that you have already said. Once it’s out of your mouth. then it’s out of your mouth. That’s why be sure while speaking.
In writing though, it already gives us enough time to review what you are saying. But in case you still messed up, you can still go back and re-edit it. However, that’s only possible if your writing is still in your hand. If you give it to someone else, just remember writing is pretty durable!

So, what's the verdict?
Well, I would have to say- It depends.
Now, don’t get angry with me! It really depends!
For eg, if your job is being a writer, well then you gotta be good at writing. On the other hand, if you are a politician then your speaking skills matter more.
So professionally, I would say it depends on what you are currently doing.
In your personal life though, I have to say that speaking matters more ( and for the same reasons, listening too!). With your family, I am guessing you will probably be speaking more rather than writing as the form of communication, so you gotta up your speaking skills for this one buddy!
The good news is- you can improve both your speaking and writing skills. You just have to work at it.