Why particles, such as the electron exist, why we have the particles we observe, why they have certain characteristics and not others, why all particles exhibit 'wave particle duality', is because...well, it's just that way!
Good suggestion from Nugatory to read about the double slit experiment. Richard Feynman said that if you really understand the double slit experiment, you know everything about quantum mechanics.
A couple of quotes from other discussions I saved from other discussions which may help:
Particles appear in rare situations when they are registered... The trouble with the particle concept is that one cannot attribute a permanent existence. It only exists at the moment it is detected.
The prior comments mean that electrons [and other particles] are modeled mathematically as to usually exist as waves except when we detect them in some measuring device. This means electrons behave as extended entities most of the time but when we detect them, when we measure them, they appear as local, point entities, or [local] quanta...that is, what we commonly call 'particles'. These are the individual 'blips' in the 'double slit experiment'. There is a brief current discussion here
https://www.physicsforums.com/showthread.php?t=703021
"mechanism behind photon absorption and photon emission"
which might also give you insights. The third post discusses the analogy between a vibrating string and an electron as a'wave'...in other words, as an extended entity. In this model, the electron is thought of as an extended vibrating wave rather than as the point particle of the old [outdated] Bohr model.