Why should a new partner contribute towards goodwill on his admission?

The goodwill existing for the business at the time of admission of new partner has been built by old partners. Thus new partner acquire the right to share the future profits and this include the capability of the partnership to general same or more profits. Thus the new partner must acquire this right by contributing towards goodwill in his profit sharing ratio.

New Partner will contribute towards Goodwill because Old partners have done hard work in the past to identify their business  product and due to this their business and its product has reputation in the market and it will earn more as compared to new business and this due to Goodwill which old partners have generate, so new partner will contribute some amount towards goodwill to compensate old partners.

As per bookish term we can say that goodwill means the 'good name' or the reputation earned by a firm through the hardwork and honesty of its owners. In one line we can say that goodwill is the extra earning capability of a firm in a competitive market situation. To creat the reputation the partners made  their efforts. So when ever a new partner is entering the business, he will have the privilege to use the goodwill of the firm which was created by the old partners. He doesn't has to make any effort to creat the goodwill. For this reason he has to contribute towards the firm's goodwill for using it. 

In short we can say that the new partner can avail the reputation of the firm only when he purchase  his share of goodwill from the old partners or pay premium of goodwill to the old partners.