The piano can only play certain fixed notes in a particular scale, whereas the human voice can hit any frequency within a certain range (or ranges). There are quite large gaps between the frequencies of adjacent notes on a piano, whereas human speech typically involves much subtler frequency variations than the piano is capable of. It would be possible to get closer to a frequency graph of human speech with an instrument that is not restricted to discrete pitches, such as a fretless bass or an Erhu.
Even then, hitting the correct pitches isn't the only requirement - you'd need to be able to articulate the volume envelope of human speech too. Between those two requirements, it's quite tricky to do, as the typical intonation of most human languages involves both subtle and large variations in both pitch and volume.
Of course there is also the timbral aspect, and the fact that human speech involves some unpitched elements - but if you want to match those as well, you probably aren't going to trying to do so on any traditional instrument (other than the human voice itself, of course!)