When the Prophet (SA) asked him if he would abandon him at this stage...
When the Prophet (SA) asked him if he would abandon him at this stage, Jibrael (AS) excused himself and assured him that only the Prophet (SA) was given the permission to proceed due to his exceptionally great rank in the eyes of Allah (SWT). Hence, Jibrael (AS) was well aware that the Prophet (SA) has attained a very high station as well as his AhlulBayt (AS) whom he had witnessed their holy names inscribed near the Throne of Allah (SWT).
Yet, Jibrael proceeded to make that request to join the AhlulBayt (AS) under the cloak in this very blessed gathering. The only thing he seeks is proximity and service of the chosen ones whom Allah (SWT) has raised their station above all stations. He recognized the fact that when a creature associates himself and draws himself closer to that which is honorable and esteemed, then he also will benefit by his association to that pure good.
Jibrael (AS) requested to become the “sixth member” even though he knows very well that the members of the cloak are only five without an addition. As a side note, it is worth reflecting on the fact that angel Jibrael (AS) sought the permission of Allah (SWT) and the permission of the Prophet (SA) to enter his house.
Now compare this example with that of certain companions of the Prophet (SA) who with all audacity barged in the house of Lady Fatima (AS) without her permission and against her will, as they intentionally squeezed her behind the door causing her immense pain and abortion of her unborn child and setting her house on fire! May Allah (SWT) punish the transgressors and enemies of the AhlulBayt (AS)!
Allah’s answer to Jibrael’ s request was an approval and a granted permission for him to join the Prophet (SA) and his AhlulBayt (AS) under the cloak! The divinely-bestowed infallibility which Jibrael (AS) has (as an angel) from committing disobedience may be a reason why Allah (SWT) qualified him to join the blessed caravan of the Prophet (SA) as there is no harm in him being an addition to this gathering.