"Ik praat niet tegen jou, maar tegen de neushoorn."
Translation:I am not talking to you, but to the rhinoceros.
Technically. Dutch uses quite a few of these compounded elements. Learning these combinations will likely be a tremendous help in your studies.
'praten tegen' = to talk to [someone]
'praten met' = to talk with [someone]
'praten over' = to talk about [someone/something/etc.]
Usages of 'praten tegen' and 'praten met' could (roughly) be considered as:
'praten tegen' -- the telling (or possibly lecturing) of something to someone
'praten met' -- more of a 'mutual' chat/discussion
To 'speak against' something/someone... that could be interpreted in quite a few ways.
Here are a few compounded elements that generally mean 'to oppose, to contradict (these are obviously beyond the scope of this lesson, and they may become used in certain contexts when another would not, etc)':
'in tegenspreek zijn met' - to contradict, oppose
'zich afzetten tegen' - to oppose, to resist
'bezwaar hebben tegen' - to reject (something)
praten/spreken tegen = to talk/speak to
"Ik praat niet tegen jou, maar die appel wel"
I am not talking to you, but (I am talking to) that apple.
"Ik praat tegen hun morgen."
I (will/shall) talk to them tomorrow.
When the discussion is more or less a 'one-sided discussion' (e.g. someone talking to themselves, animals, etc.) or someone addressing a statement/making an announcement or declaration/etc. -- to someone or several people -- and then, perhaps, leaving the room immediately after saying what they needed to say; then the use of 'praten tegen' (to speak to) may suffice.
praten/spreken met = to talk/speak with
This would encompass general talking between two or more individuals.
"Ze zitten met elkaar te praten." They are (sitting while) talking to each other.
The use of 'spreken' in place of 'praten' in most of these cases could be rendered as more formal.
(there is more I plan(ned) to type but I am falling asleep at the keyboard ;))