In a multidimensional array, you can change only the last dimension when you use Preserve. If you attempt to change any of the other dimensions, a run-time error occurs.
A part from this your code is really suboptimal because you are planning to Redim you array at every loop. Redimming with preserve is worse because not only the runtime allocates a new array but it should also copy from the old array to the new array.
In your case is better to declare a simple class like this
Public Class CategoryInfo
Public info1 As String
Public info2 As String
End Class
then use a List(Of CategoryInfo)
Dim infos as List(Of CategoryInfo) = new List(Of CategoryInfo)()
While reader.Read()
Dim nf As CategoryInfo = new CategoryInfo()
nf.info1 = reader.GetString(0)
nf.info2 = reader.GetString(1)
infos.Add(nf)
' if you like the all-in-one-line coding style you could also write the above in this way
' infos.Add(New CategoryInfo With {.info1=reader.GetString(0), .info2=reader.GetString(1)} )
End While
Now, if you really need to have your data inside a string array you could write
Dim categoryInfo(infos.Count, 2) as String
for x = 0 to infos.Count -1
categoryInfo(x,0) = infos(x).info1
categoryInfo(x,1) = infos(x).info2
next
this is still not very optimal because you loop two times on your data but, at least, it will get your data as you want.