Counterspell causes a spell to fail and a scroll to be consumed
Counterspell works differently than just stopping a spell casting or scroll reading.
“Fails and is wasted”
Jeremy Crawford recently responded directly to a question about counterspelling a spell scroll:
Marc Sharma asked:
@JeremyECrawford If a spell cast from a spell scroll is counterspelled, does the scroll lose its magic as if the spell was cast?
When successful, counterspell foils a spell that is cast. The casting isn't undone. The spell fails and is wasted.
The language used is general, because counterspell works similarly regardless to the mode of spell casting. It wastes whatever resources were used to cast it, whether that’s a spell slot, a spell scroll, a daily use (for monsters) — and in any case, the action (or bonus action or reaction) used to cast the spell.
The general case: normal interruption of spells and scrolls
When a caster simply stops casting a spell before finishing, a spell slot is not expended.
When you cast a spell with a casting time longer than a single action or reaction…if your concentration is broken, the spell fails but you don’t expend a spell slot or scroll:
PH p. 202, Longer Casting Times
Edits to the DM Basic Rules have specified that spell scrolls work the same way:
If the casting is interrupted, the scroll is not lost.
DM Basic Rules, p. 60
The wording for scrolls is a little different, but the results are the same. If you simply stop casting a spell or reading a scroll before completing it, it’s as though you had not started.
The rules errata simply make it clear that reading from a scroll works like casting a spell in any other way, in this regard.
“The spell fails, but…” vs. “The spell fails, and”
The word but in the errata about interrupted spells calls out that this is a special case. In general, spell failure entails expending of a spell slot, or scroll, without causing a spell effect, as when failing to cast a higher-level spell scroll:
On a failed check, reading the scroll only consumes its magic with no other effect.
Or in Crawford’s tweet:
The spell fails and is wasted.
DM Basic Rules, p. 60
Counterspell resolves a spell and replaces its effect
Counterspell does more than just interrupt a spell’s casting. When Counterspell is successful:
“The spell fails and has no effect.”
PH, p. 228. Emphasis added.
This phrase is used 3 times in the spell description; it’s key to understanding the spell. The spell is not just interrupted, it completes, fails (without “buts”) and its effect is negated.
Only a completely cast spell has an effect to negate, so Counterspell does not stop a spell before it’s cast. Then, “once the spell is cast, the words on the scroll fade, and the scroll itself crumbles to dust.” (DM Basic rules, p. 60)
Interrupting the casting is a relevant, separate effect of Counterspell
The fact that Counterspell interrupts a casting is relevant when the spell has a long casting time: you don’t have to wait until a spell is about to resolve to counter a spell. This is why Counterspell both interrupts a spell’s casting and then causes the spell to fail.
The Original Misunderstanding
A historical note, I suspect the original misunderstanding about whether a spell scroll is used up while it is being read comes is based on some “color text” in found in first edition AD&D:
As a spell is read from the scroll, its letters and figures writhe and glow, the magic is effected, and then the lines fade and are gone forever
This passage appears on DMG p. 117, AD&D 1e, 1979 Revised edition, and DMG p. 118, AD&D 1e, original printing.
The rules errata make clear that if a some modern spell with a longer casting time is interrupted normally, the resources that went into casting it are not wasted. This normal interruption of spell casting is different than Counterspell.
Optional rules for this can be found in Xanathar's Guide to Everything
On page 85 (or on D&D Beyond) there is a section on "Identifying a spell" that reads:
It goes on to explain in detail what checks are involved (not transcribing everything here for copyright reasons). Do note that the rules presented in Xanathar's are considered optional/variant rules.
Using these rules with Counterspell
Unfortunately these rules do require a reaction to identify the spell being cast which means that your reaction is expended and you can't usually use this along with Counterspell if you are alone, unless the spell is being cast over several rounds.
You might be able to achieve this with two characters: one of them identifying the spell for the other to cast counterspell.1 (A strict reading of the rules may not allow speaking outside your turn, see this Q/A. However, I have never played with a DM that actually enforces this.)
Jeremy Crawford has also addressed this issue (though unofficially) in a series of tweets found on this Sage Advice page2. Notably, these two exchanges are of particular interest:
And then again later on:
So it seems that though unofficially, Jeremy Crawford also subscribes to the idea of allowing one person to identify a spell and telling another so they can counterspell (at least as of the writing of this answer).