Jews in Iraq had been persecuted throughout the 1930s and they suffered a major pogrom in 1941, known as the Farhud.
This persecution continued throughout the decade, as this 1961 Israeli MFA article (that skeptically mentions the swap offer) notes:
How the Jews of Iraq Became Refugees
An eye-witness account, written by a visitor from overseas early in 1949 shortly after the conclusion of the Arab war against Israel, presents a graphic picture of the position of Iraqi Jewry at that time: “The Jews of Iraq” it stated, “are in a state of panic. They have been attacked in the streets, have had their businesses broken into and an alarming number have been murdered in cold blood. They have been dismissed from all branches of public and civil service, must submit to a curfew every evening and have been barred from most of the general amenities available to the ordinary citizen. Many have made desperate attempts to escape, but without success.”
When the United Nations Economic Survey Commission for the Middle East visited Baghdad in October 1949, the then Iraqi Premier was reported to have proposed that 100,000 Iraqi Jews out of some 160,000 to 180,000 be sent to Israel in exchange for 100,000 Palestine Arab refugees. The Jews were to leave their property in Iraq and take over the property in Israel of 100,000 Arabs. If this suggestion of a population transfer and mutual financial compensation was really made, it was soon dropped by the Iraqi Government. It was apparently found easier to terrorize the Jews into leaving by fixing a time limit for their departure and enacting legislation to seize their possessions for the benefit of the Iraqi exchequer.
In the third week of December 1949, a second wave of anti-Jewish pogroms began. Thousands were imprisoned on charges of “Zionism” or taken into “protective custody.” When, as expected, large numbers thereupon applied for exit permits to Israel, legislation was rushed through freezing Jewish accounts in the banks and forbidding the sale of property without special permit. Jews were permitted to leave with only 50 kgs of luggage per person. On 10 March, 1950, the Iraqi Government issued a decree blocking the property of all Jews who, on leaving the country, “had relinquished their nationality.” A special custodian of Jewish property was appointed, who began immediately to sell it by public auction.
To speed up the departure of the Jewish community, the Iraqi Government set a time limit for it, fixing 21 June as the final date. As a further incentive a series of laws was enacted designed to make the position of the Jews in the country untenable. Restrictions were imposed on their movements. They were barred from schools, hospitals and other public institutions. They were refused import and export licences for carrying on their business. At the same time the arrests continued. So effective were these oppressive measures that by mid-July 1950 over 110,000 Iraqi Jews had registered for emigration and by June 1951 had left for Israel. By the end of 1951, the number of Iraqi Jews transferred to Israel amounted approximately to 125,000. Most of them were brought over by chartered aircraft. They arrived utterly destitute, carrying small bags which held all their belongings. Such was the end of what had been for centuries the most prosperous and cultured Jewish community of the East--a community which could trace its history back for more than 2,000 years, centuries before the Arabs had come to Iraq.
And, no, the anti-semitic slander that Jews were behind some of the anti-Jewish attacks in Iraq at the time has been proven a lie.
Anyway, the offer itself is most intriguing. Chances are that the Arab League at the time forced Iraq to withdraw the offer in order to keep the refugee issue festering, the way that Arab leaders had been doing for decades.
But imagine if Iraq's initial 1949 offer had been matched by Egypt, Syria, Lebanon and the Gulf states.
The refugee issue would have been solved sixty years ago.