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)
In short & generally:
Praten - to talk
Spreken - to speak
'Spreken' in the sense of 'to talk' is more formal. It could also render 'to give a talk' (e.g. a person giving a talk/speech to a group of people; a preposition may also need to be added as well- depending on context, intent, etc.)
"Talking with" someone is a-ok. It simply implies a conversation. The dictionary says, "To talk with someone means simply 'to discuss' or 'to give someone a message,' as in 'We talked with her about her plans.'"
My favorite explanation of the difference in English though is Grammar Girl's: http://www.quickanddirtytips.com/education/grammar/talk-with-versus-talk-to.
As a native speaker, I'd say there's a simple distinction - British English speakers usually say "talk to" someone, American English speakers usually say "talk with" someone.
As is normal with a predominant usage, the American English usage of "talk with" is becoming more common in British English (I'd almost never heard it in Britain until about 10 or 15 years ago).
I am a native American English speaker, and my grandparents were native Dutch speakers. I use either "talk with" or "talk to" depending on the situation. Like, if I need to say something about someone's behavior or am speaking about an upcoming meeting/event, I "talk to" them. If I am just having a conversation, I am "talking with" them.
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 ;))
What is wrong about "I'm not talking about you but about the rhino"? "About'' is given as a second choice in the hints without any amplification or warning that it might be wrong. DL sometimes does this and it's quite annoying. In another case recently, I chose the first word in the hint and DL marked it wrong and used the second hint word as the correct answer. Logic of this?