You're arguing semantics at this point.
Handhelds have a different demographic than consoles similar to mobile gaming. Both are part of the videogame market but what made the PS4 successful differ from what made the DS successful. Just look at the difference in price, technology, portability, third party support, or even IP's like God of War & GTA that were made for the PSP. What do you think happens if the 3DS is priced the same as the PS4 at launch? What about if the PS4 dropped below $200 like the 3DS for the majority of its time on the market?
"You're arguing semantics at this point"
Well, whenever you have an argument about definitions it is an argument about semantics. So we are both arguing semantics.
"Both are part of the videogame market"
I'm glad we can agree on this
"What do you think happens if the 3DS is priced the same as the PS4 at launch?"
I don't understand what this has to do with why "consoles" excludes handheld consoles. Home consoles and handheld consoles are different, yes. Console's without the qualifier just means any videogame console. Home consoles means home, handheld consoles means handheld, consoles (or videogame consoles specifically) means all of the above.