Basically I think that Hamas as an organisation have no rights to exist. Logically they deny their own history. In order to prove this, first we need to know what they stand for as an organisation.
Hamas is an acrorym for Harakat al-Muqawama al-Islamiyya or in English, Islamic Resistance Movement; it's also the Arabic word for "zeal". Hamas seeks to establish an Islamic theocracy in the area that is currently Israel, the West Bank, and the Gaza Strip. In pursuit of this end, Hamas affirms a right to engage in armed struggle.
Abdel Aziz al-Rantissi, a co-founder of Hamas, reportedly stated that the movement's goal is "to remove Israel from the map". While during the 2006 election campaign Hamas dropped its call for the destruction of Israel from its manifesto but several Hamas candidates insist that the charter is still in force and often called for Israel to be "wiped off the map" in their campaign speeches. Their main assertion is that the land currently held by the state of Israel was stolen off them in 1948 and that it should return to the state before then.
What was that state?
The area of Palestine was invaded by the Romans and set up King Herod as a Jewish figurehead king in 19BC, with his death in 6BC or thereof the state was then under direct Roman rule. The city existed like this until 70AD when during riots it was razed.
When the Roman Empire snapped in half in 330 it became part of the Eastern Roman Empire and then when the Ottomans assumed control in 1453, it remained that way until the breakup of that empire until 1917 when the British took over under the Balfour Declaration.
In 1922 the area was again split into the Hashemite Kingdom of Transjordan (which still exists) and Palestine which comprised both modern Israel and Palestine. This split was as a result of the Balfour Declaration and a set of plans were drawn up for a further constitution known as the Palestine Mandate.
Article 2 of the Palestine Mandate stated that the administration would "secure the establishment of the Jewish national home", while "safeguarding the civil and religious rights of all the inhabitants of Palestine".
In addition, Article 25 of the mandate stated that all territory east of the Jordan was, in most part, at Britain's will, withheld from all provisions of the mandate.
In 1948 it was decided to repatriate Jewish peoples to their homeland after the terrible atrocities of the Nazi regime in Germany. This was signed by the governors of Palestine who at the time consisted of 12 Arabic and 12 Jewish leaders.
Therefore the fact that Hamas in principle wishes to deny the existance of the state of Israel, actually by inference denounces that they should have the right to exist themselves. The conditions which created Israel actually gave rise to their own homeland which in 1922 was never invisaged.
There could be another reason - Palestinians hate the Jews and have elected terrorists as their government.