We use אלא when we want to refute a statement which is totally false in our opinion.
I don't like apples, but oranges = אני לא אוהב תפוחים, אלא תפוזים
The conjunction אבל and אך are basically the same, except that "אך" is considered to be more formal.
We use אבל and אך when we want to refute a statement but we do have something more to add about it which is (usually) relevant.
They don't like soccer, but they do like sports = הם לא אוהבים כדורגל, אבל הם כן אוהבים ספורט
I appreciate BartiBar's clarifying points. My understanding is that the contrasting conjunction אלא ("but rather") is not classical Hebrew. It came into Hebrew through Aramaic (it's attested in Palmyrene, Qumran, Jewish Palestinian Aramaic, Christian Palestinian Aramaic, and Syriac). In Jewish Babylonian Aramaic of the Bavli it's sometimes spelled אילא, while in Mandaic it's spelled עלא. It's not originally connected to Gk ἀλλά, but in areas of strong hellenistic influence אלא was likely replicated sometimes to some extent on ἀλλά. Similarly, in places where Arabic became the dominant language, there may have been a similar Arabic influence on the meaning of אלא through إلّا. See Blau's Dictionary of Judeao-Arabic Texts (Academy of Hebrew Languages, 2006), entry on אלא // إلّا, pp. 15-16. It's interesting that אך is considered more formal in modern Hebrew (it's used as an adversative particle in classical Hebrew and the Hebrew of Ben Sira). I don't have a good feel for how these terms are used in modern Hebrew but BartiBar's note is a helpful start.
Sorry. "לא אני, אלא הוא!" seems to be the answer to a question, ie "who did this?" and the answer, grammatically correct, would be "not I, but he." (nominative case). Had the question been, "Whom did they accuse?" the answer would be "not me. but him" (accusative case). Maybe "לא אותי, אלא אותו’
IT IS EITHER NOT ME, BUT HIM, OR NOT I BUT HE, THE SECOND SENTENCE BEING TRULY AWKWARD, BUT ALSO INCORRECT.
IN ANOTHER INSTANCE, MY ANSWER WAS " I EAT PIZZA AND THEN I READ A BOOK." THAT WAS MARKED INCORRECT.
THE SECOND CORRECT ANSWER PROPOSED WAS" I EAT A PIZZA AND THEN I AM READING A BOOK." , WHICH IS INCORRECT, BECAUSE IN THIS CASE, IN ENGLISH, BOTH VERBS MUST AGREE, THAT IS,THEY MUST BOTH BE THE SAME TENSE OR MODE, AS THE SUBJECT IS ONE AND THE SAME. ANOTHER FACT IS THAT PIZZA IN ENGLISH IS UNCOUNTABLE OR COUNTABLE, SO EITHER "A PIZZA" OR JUST "PIZZA" IS CORRECT IN THE CONTEXT. I HOPE MY COMMENT PROVES USEFUL. I AM GRATEFUL AND HAPPY WITH ALL MY DUOLINGUO LANGUAGE COURSES. THANKS DUOLINGUO, AND THANKS AS WELL TO ALL THE MARVELOUS LANGUAGE TEACHERS SUPPORTING IT.
Sorry. Now I am using my English keyboard. But when I have the Hebrew keyboard activated I can't easily switch from one to the other, so I use the one lower case for Hebrew and the upper case for English. Sorry. I am nit very good at typing!
Are you using a computer or a phone/tablet? If you are using a device with a virtual keyboard you can just switch it easily with an app. I use Swype, and have four languages on it. I switch them by holding / pressing down the space bar for a second and I can choose from my list. If you are on a computer, it depends on the type but there is an option for that too. Let me know if you need help, it seems like it would be a pain (and complaints) to continue long-term using uppercase for English. (I also bought a silicone Hebrew keyboard cover to use with my computer for $10 - but really find my tablet and "swiping" easier).
Languages are conventional and there is no one-to-one word correspondence from one language to another. Just learn it as it is and try not to compare the structures but to associate the Hebrew statements to their English wording as they appear.