Gemara: One day the three [candidates for conversion, who were rejected by Shammai and accepted by Hillel] happened to be in the same place. They said: The kapdanut (exacting, intolerant nature) of Shammai attempted to have us lose our place in the world, and theanvatanut (humility, patience, tolerance) of Hillel brought us close under the wings of the Divine Presence.

Ein Ayah: Everyone has a preparatory track ready for the shleimut(completeness) that is destined for him and has everything that he needs to reach his highest potential. The shortcomings that are liable to undo the spirit and cause it to look for that which it desires are also planted in the nature of the spirit in a way that negatively parallels the potential for spiritual advancement. There are some shortcomings that are found only in those who have the potential for certain types of advancement.
There are righteous people among the nations of the world who never convert and are happy with their level and more limited obligations. However, one who is prepared for the lofty level of enteringKlal Yisrael also has dangerous shortcomings ready for the possibility that he will not reach his potential and convert as he was designed to do. That is the reason that Shammai’s exacting nature not only did not allow the candidates to advance but also threatened to lower them beneath the level at which they started, as upstanding gentiles. As those with the potential and interest in conversion, missing out on the opportunity would have been very bad. They could have missed out on even levels that simple non-Jews, with no aspirations of conversion or any other great spiritual dreams, have. They could have dropped to the lowest levels of moral waste.
In contrast, Hillel’s humility not only saved them from deterioration but brought them to spiritual safety. This was not by means of simply remaining a fine non-Jew but by the eternal and lofty clinging to Hashem by joining His covenant.
When the three of them came to the same place and reflected on being pushed away by Shammai and being drawn close by Hillel, they came to a joint conclusion. They realized that there are two reasonable approaches, and one cannot say that there is no value in Shammai’s approach. Given the greatness of Shammai as a person and the fact that he had a consistent, thought-out policy, it must have had value. There must be cases for which the absolute demand for high standards is useful.
They did not say that Shammai pushed them toward deterioration or that Hillel drew them close but that their approaches did, for the focus was on the approach, as opposed to the person. Actually, to maintain that which has already been acquired by the individual and the nation, high standards and discipline contribute a lot to keeping away corruptive influences. However, in order to make new acquisitions, for the individual or the collective, or to return that which has been lost, including bringing in people from the world at large, one has to use theanvatanut of Hillel.