What is the matter with Iran and Israel?

I guess we can all agree that the relations between Israel and Iran aren't the best:

Of course that list is just a few examples.

So what is the reason behind all that?

• Is there some real grudge behind that conflict explainable by some tangible reasons? AFAIK international politics is mostly explainable by hard reasons, mostly about influence and power, not some irrational emotions (Exceptions do exists)
• Does the Iran supplies the forces hostile to Israel because he has sympathy for their cause? Or does he wants to have some leverage against the USA should they try a second Operation Ajax?
• Is it just a setup from hardliners on both sides to enjoy interior power by having an foreign enemy?
• According to en.m.wikipedia.org/wiki/Iran–Israel_relations relations were good during the time of the Shah. – Andrew Grimm May 10 '17 at 10:30
• Israel is convenient foe for the authoritarian Arab leaders. That's pretty much it. – JonathanReez May 10 '17 at 11:33
• @ Andrew Grimm - That isn't surprising, considering the Shah of Iran was a U.S. puppet. (Interested readers should read about SAVAK.) That's why he was overthrown in a revolution. Yet even the Shah had some harsh words about Israel and the "American Jewish Lobby" -- youtube.com/watch?v=6kySR3fpa5s @ JonathanReez - That's like saying "North Korea is a convenient foe for South Korea." Israel is hardly innocent. As one of many examples, Israel assassinates Iranian nuclear scientists when Israel itself has (illegal) nuclear weapons. – David Blomstrom May 10 '17 at 22:56
• Regarding Ahmadinejad's threat -- washingtonpost.com/blogs/fact-checker/post/… – David Blomstrom May 10 '17 at 22:56
• @David do you have a citation about nuclear weapons being illegal? – Andrew Grimm May 11 '17 at 2:07

Iran's side:

1. Geopolitical reasons

• Depending on your view, Iran has aspirations of regional hegemony or opposition to other's regional hegemony (be it US hegemony or Sunni KSA-led one).

In either case, opposing Israel helps on two axis here:

• Israel is seen as being on opposite side of that goal

• Being "most anti-Zionist" scores cookie points for Iran with all Moslem populations, not only allied Shia but even Sunnis.

2. Domestic reason #1: external enemy helps the government.

• Objectively, having a known public strategic enemy is good for any government. You can blame any issues on them; you can distract population from domestic issues by whipping up anti-enemy sentiment and focusing the ire on the target. Israel is ideal for the purpose, as explained below.
3. Domestic reason #2: Populace dislikes Jews and especially Israel.

• Iran's government considers USA as a "Great Satan". Israel - correctly - is perceived in the Middle East, including in Iran, as USA's bulwark in the region (or lapdog, if you take the opposite side). Iran has no way to directly hurt USA and is worried about reaction if they do (nobody wants to end up like Saddam or Taliban); so proxying that to Israel is a good strategy.

• Thanks in large part to Mohammad Amin al-Husayni; Muslim populace in 20th century dislikes Jews (that hate long preceded 1967 war; and even creation of Israel in 1948; so blaming it on "occupation" is falsehood, though a convenient one). As such, warmongering against Israel plays very well domestically in Iran.

• Additionally, Iranians dislike Israel due to friendly relations Israel had with the Pahlavi Shah.

4. Ideological reasons

• Many in Iran welcome the idea of religious war with the West based on the concept of the return of the 12th Imam . Conflict with Israel is seen through that lens as desirable.

Israel's side:

1. Geopolitical reason #1 - Iran is a threat

2. Geopolitical reason #2 - Iran is a credible threat on its own.

While Iran would struggle to be more than an annoyance to USA purely militarily (depending on methods, a threat via attacking shipping in Hormuz Straight or having its terrorist proxies attack US interests elsewhere is more effective); it has a large army and military-industrial base (100M populace and plentiful oil); and therefore presents a credible strategic threat even conventionally to Israel.

Couple that with potential nuclear weapons, and a compact small country like Israel has a threat that is not only credible but existential - it doesn't take too many nukes to wipe ALL of Israel off the map.

3. Geopolitical reason #3 - Iran is a credible threat through its terrorist proxies.

Iran successfully funds and trains terrorist proxies, most notable and importantly, Hezbollah (Iran also funds and tries to arm Hamas in Gaza).

Hezbollah poses a significant threat to Israel, especially armed with Iranian rockets. And of course israel as a democratic country is vulnerable to in-country terrorist attacks, though less so due to decades of experience of terror threat.

4. Domsetic reason

While there are rational reasons for Israel to be concerned over Iran (see above); we can't discount the fact that Iran is useful in domestic politics - just as Iranian govrernment can use Israel as distraction for its citizens, so can Israel's government use Iran for the same purpose (corruption investigation against Prime Minister? BUT IRAN!!!...)

• You say an "external enemy" helps Iran. Ditto for Israel. You say Iranians dislike Jews, especially Israel. The opposite is also true. You say Iran poses a threat to Iran. Take a look at Iraq, Syria and Libya, then ask yourself if Iran feels threatened - especially when 1) Israel has nuclear weapons, and 2) the U.S. has been playing games (including economic sanctions) with Iran for many years. Under "Ideological Reasons," you mention the return of the 12th Imam, a reminder that Iran is a theocracy. In a similar vein, it's worth noting that Israel is a de facto theocracy based on Zionism. – David Blomstrom May 10 '17 at 23:04
• Domestic reason #2: Populace dislikes Jews ... -- youtube.com/watch?v=dUP571KQyRQ – user4514 Sep 8 '17 at 13:37

Ideology:
War with leaders of the disbelief (Imams of kufr), i.e. Those who have all of the following properties "infidels, leading and spreading infidelity, and dont adhere treaties", is a religious duty.
(Quran;9/12) But if, after coming to terms with you, they break their oaths and revile your belief, fight the leaders of the disbelief for they have no oaths in order that they will desist.

Iran supply Hezbollah (which is Shia) and Hamas (which is Sunni) against Israel, because Iran consider Israel as occupier of Muslim lands and murderer of them.
Imam Khomeini, founder of Islamic Republic of Iran, was enemy of Isral, even 15 years before revolution victory. he accused the Shah of submission to the United States and Israel.

Racism:
Iran was against apartheid in south Africa, because of racism, too. Iran recognize Israel as racist.

Public beliefs: