I'll flag the issue with that sentence in the Tatoeba forum, and drop the sentence from the main example for sense 3. I'll also add an alternative sense 3 example.

the japanese sentence was 愛すればこそ彼女と結婚したかった before it was changed mistakenly. this can be seen from the tatoeba logs.
if you change it back, you only need to add an english translation to it.
"It was because I loved her that I wished to marry her."

愛すればこそ彼女と結婚しなかった。 I didn't marry her because I loved her.

I believe the sense 3 sentence is a mistranslation. (To me, at least) the English is saying "Love wasn't the reason I married her" whereas the Japanese means "It was because I loved her that I didn't marry" (which doesn't make much sense). Presumably the English sentence is the original, so the Japanese would need to be changed (preferably by a native speaker). A pity we'll lose an example for sense 3, though. Could we add another one? Something like "君の将来を思えばこそこう言ってるんだ。It's because I'm thinking of your future that I'm saying this." (adapted from a GG5 example)
I found and indexed an sentence for sense 2 (彼は年こそ若いが十分その仕事をやっていける。Young as he is, he is equal to the task. )

@@ -28,0 +29 @@
+<gloss>only because ...</gloss>

Of the 95 sentences I found one for sense 3 and none for sense 2.

gg5, daij, meikyo, DIJG

Expanding.

@@ -10 +10,5 @@
-<s_inf>emphasizes preceding word, phrase, etc.</s_inf>
+<s_inf>emphasizes preceding word or phrase</s_inf>
+<gloss>it is ... that ...</gloss>
+<gloss>precisely</gloss>
+<gloss>in particular</gloss>
+<gloss>definitely</gloss>
@@ -12,3 +16,22 @@
-<gloss>especially</gloss>
-<gloss>even more so</gloss>
-<gloss>in particular</gloss>
+<gloss>only (when, after, because, etc.)</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<s_inf>as こそあれ, こそすれ, こそするが, etc.</s_inf>
+<gloss>although</gloss>
+<gloss>while</gloss>
+<gloss>it is the case that ... but</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<s_inf>after conditional -ba form of verb</s_inf>
+<gloss>it is precisely because ... that ...</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<misc>&litf;</misc>
+<s_inf>after -nai stem of verb + ば</s_inf>
+<gloss>not at all</gloss>
+<gloss>not in the slightest</gloss>
+<gloss>absolutely not</gloss>
+<gloss>never</gloss>