Eli5 Why can’t we “know” the speed and position of an electron simultaneously? Why can we only measure one of these properties at a time?

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This always confuses me and I’m not sure how it works. Please explain…

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Schroedinger, Erwin, Professor of Physics!
Wrote daring equations! Confounded his critics!
(Not bad, eh? Don’t worry. This part of the verse
Starts off pretty good, but it gets a lot worse.)
‘win saw that the theory that Newton’d invented
By Einstein’s discov’ries had been badly dented.
What now? wailed his colleagues. Said Erwin, “Don’t Panic,
No grease monkey I, but a quantum mechanic!
“Consider electrons. Now, these tiny articles
Are sometimes like waves, then sometimes like particles.
If that’s not confusing, the nuclear dance
Of electrons and suchlike is governed by chance!
“No sweat though — my theory permits us to judge
Where some of ’em is and the rest of ’em was.”
Not everyone bought this; it threatened to wreck
The comforting linkage of cause and effect.
E’en Einstein had doubts, and so Schroedinger tried
To tell him what quantum mechanics implied.
Said ‘win to Al, “Brother, suppose we’ve a cat,
And inside a tube we have put that cat at–
“Along with a solitaire deck and some Fritos,
A bottle of Night Train, a couple mosquitoes
(or something else rhyming) and, oh, if you got ’em,
One vial Prussic acid, one decaying ottom
“Or atom — whatever — but when it emits,
A trigger device blasts our vial into bits
Which snuffs our poor kitty. The odds of this crime
Are 50 to 50 per hour each time.
“The cylinder’s sealed. The hours’s passed away. Is
Our pussy still purring — or pushing up daisies?
Now _you’d_ say the cat either lives or it don’t
But quantum mechanics is stubborn and won’t.
“Statistically speaking, the cat, goes the joke,
Is half a cat breathing and half a cat croaked.
To some this may seem a ridiculous view,
But quantum mechanics must answer, ‘Tis true!’
“We may not know much, but one thing’s fo,sho’;
There’s things in the cosmos that we cannot know.
Shine light on electrons — you’ll cause them to swerve.
The act of observing disturbs the observed —
“Which ruins your test. But then if there’s no testing
To see if a particle’s moving or resting
Why try to conjecture? Pure useless endeavor!
We know probability — certainty never.”
The effect of this notion? I very much fear
‘Twill make doubtful all things that were formerly clear.
Till soon the cat doctors will say in reports,
“We’ve just flipped a coin and learned he’s a corpse.”
So said Herr Erwin. Quoth Albert, “You’re nuts.
God doesn’t play dice with the universe, putz.
I’ll prove it!” he said, and Lord knows he tried —
In vain — until fin’ly he more or less died.
‘win spoke at his funeral: “Listen, dear friends,
Sweet Al was my buddy. I must make ammends.
Though he doubted my theory, I’ll say of this saint:
Ten-to-one he’s in heaven — but five bucks says he ain’t.”

(shamelessly stolen from Cecil Adams at the the Chicago Reader’s Straight Dope column).

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