Attenuate the low frequencies in a speech wave
As you've already figured out, you need to choose an odd filter length. I'll explain why. You're designing a linear phase FIR filter, and such filters satisfy certain symmetry conditions. See this answer explaining the four types of linear phase FIR filters (even/odd length, even/odd symmetry).

For frequency selective filters, such as the one you're trying to design, you need filters with even symmetry (type I or type II). An even length (type II) filter necessarily has a zero at Nyquist, so you can't use it to design a high pass filter. A type I filter (even symmetry, odd filter length) doesn't have this restriction, so in order to design a linear phase high pass filter you need to choose an odd filter length, i.e., a type I linear phase FIR filter.