In Romeo and Juliet by Shakespeare, how is the fast pace of our protagonists' relationship, ultimately, the reason for the tragedy?

Firstly, the two lovers emphatically believe that they are in love. Their desire for one another is so strong that they believe that living without each other is impossible. This, however, is a naive and immature assessment on their part, for their supposed love is more infatuation than anything else. Juliet has never loved before and Romeo is, to a certain extent, on the rebound. 

It is this infatuation, their immaturity and their circumstances which make the two perform rash and irrational acts. Their passion causes them to act on impulse and they do not apply logic and reason in their choices. 

In Act 2, Scene 2, Juliet does not want Romeo to swear that he loves her. She realizes that things are moving too quickly and fears that she will not enjoy the sweet promise of sharing her love with Romeo. She declares:

Well, do not swear: although I joy in thee,
I have no joy of this contract to-night:
It is too rash, too unadvised, too sudden;
Too like the lightning, which doth cease to be
Ere one can say 'It lightens.'

At this point, she is clearly wise and insightful but this moment of illumination quickly disappears when the two lovers realize that it is too difficult to take leave of one another. Once they decide to part, Juliet practically forces Romeo's hand by asking him to marry her if his love is true:

Three words, dear Romeo, and good night indeed.
If that thy bent of love be honourable,
Thy purpose marriage, send me word to-morrow,
By one that I'll procure to come to thee,
Where and what time thou wilt perform the rite;
And all my fortunes at thy foot I'll lay
And follow thee my lord throughout the world.

She promises to be ready whenever Romeo chooses and would be at his side wherever he should go. Romeo promises to send for her at nine the next morning. Their cause is not much helped by friar Laurence, who, for all his good intentions, creates more problems than solutions.

In Scene 3 of the same act, when Romeo approaches the friar and requests that he perform the marriage ritual, he is much too obliging and acquiesces to Romeo's request. He agrees because he believes that their union may put an end to the feud between the two warring families.

But come, young waverer, come, go with me,
In one respect I'll thy assistant be;
For this alliance may so happy prove,
To turn your households' rancour to pure love.

This belief soon proves to be a naive and irrational error on the friar's part. He joins the two in matrimony at the end of the final scene in Act 2.

Events succeeding the two star crossed lovers' marriage soon create a crisis. After Romeo avenges Mercutio's death by killing Tybalt, their problems are compounded. Romeo is banished at the risk of execution by Prince Escalus and he cannot, therefore, be with Juliet and consummate their marriage. The friar, however, advises that Romeo visit her secretly that night and then flee to Mantua before dawn. He would then gather friends of the two lovers together and they will then request a pardon. Once it is granted they will publicly make known their love.

Things, however, do not work out as planned, for Lord Capulet has arranged for Juliet to marry the county Prince that Thursday. Once again, the friar finds a way out of the mess he had helped create but, unfortunately, his plans do not entirely work as he so foolishly thought they would. The friar, just as much as the two heartsick lovers, did not consider all their options and things go horribly wrong.

The friar had arranged for Juliet to drink a potion which would put her in a death-like sleep. Her parents, thinking that she had died, would bury her in the family vault. She would awaken later and Romeo would be at her side. The two would then easily escape to Mantua and no one would be any the wiser. Unfortunately, the friar's urgent letter to Romeo setting out the above, never reaches its destination due to an unfortunate event in which the messenger is held captive to avoid the spread of an infectious disease.

Romeo learns, wrongly, that Juliet has died and secretly returns to Verona after having purchased a deadly potion with which to commit suicide. He visits the crypt and sees what he believes is Juliet's corpse. He then kills himself by swallowing the poison. When Juliet awakes she sees his lifeless body, takes his dagger and kills herself.

If the two lovers had just practiced patience, none of these unfortunate events might have occurred. However, one can also argue that the actual turning-point in the drama was not so much their marriage, but the deaths of Mercutio and Tybalt, which changed the course of events completely.