Parasurama was not the incarnation (Avatar) of Lord Vishnu

According to Puranas, Parasurama was the 6th incarnation of Lord Vishnu.  He makes a brief appearance in Srimad Ramayana in penultimate Sargas of Bala Kanda.

His story, in his own words, as described in those penultimate Sargas of Bala Kanda of Srimad Ramayana is as follows:

Vishnu handed over a supreme bow to Sage Riciika, the son of Bhrigu, as a trustworthy trust.  That great-resplendent Sage Riciika on his part has handed over this divine bow to his son with unmatchable deeds of religious merit, who is my father Sage Jamadagni.

Adhering to a barbarous mentality Kaartvaviirya Arjuna put my father to death, when the ascetically powerful father of mine has isolated himself from arsenal.

वधम् अप्रतिरूपम् तु पितुः श्रुत्वा सु दारुणम् |
क्षत्रम् उत्सादयन् रोषात् जातम् जातम् अनेकशः ||
पृथिवीम् च अखिलाम् प्राप्य काश्यपाय महात्मने |
यज्ञस्य अन्ते तदा राम दक्षिणाम् पुण्य कर्मणे ||
दत्त्वा महेन्द्र निलयः तपो बल समन्वितः |

श्रुत्वा तु धनुषो भेदम् ततो अहम् द्रुतम् आगतः ||
तत् एवम् वैष्णवम् राम पितृ पैतामहम् महत् |
क्षत्र धर्मम् पुरस् कृत्य गृह्णीष्व धनुर् उत्तमम् ||      (Bala kanda 75^th Sarga 24 -27 Slokas)

 “On hearing the unregenerate and highly perfidious murdering of my father, I rancorously extirpated Kshatriya-s as and when they are born, that too not for one time, going around the earth... and on getting the entire earth under my control I performed Vedic-ritual, and at the end of that Vedic-ritual, I gave all that earth to sage Kashyapa, a sage with divine soul and with pious observances, as a ritualistic-generosity... and I am at present on Mt. Mahendra practising ascesis and thus conjoined are the powers of ascesis in me."

"On hearing about the breakage of Shiva's longbow, then I promptly came here. Thereby, oh, Rama, wield this supernatural and superlative longbow of Vishnu, which is passed on to me from my forefathers and my father. Keep your fealty to Kshatriya-hood in view, and wield this as you have wielded Shiva's longbow”

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The Story of Parasurama also appears in Mahabharata, wherein it was mentioned that Drona obtained all his divine weapons from the former.  

Drona heard that the illustrious Brahmana Jamadagnya, Rama the son of Jamadagni, had expressed a desire of giving away all his wealth to Brahmanas. Having heard of Rama's knowledge of arms and of his celestial weapons also, Drona, who set his heart upon them as also upon the knowledge of morality that Rama possessed, set out for the Mahendra mountains.

Arrived at Mahendra, Drona approached Rama the son of Jamadagni, worshipped Rama's feet, and told him that he came there with the desire of obtaining his wealth.'

On hearing him, Rama said that he gave away his gold and whatever other wealth he had to Brahmanas! He further stated that the earth also, to the verge of the sea, decked with towns and cities, as with a garland of flowers, was given unto Kasyapa. And, he added that he was left with his body only and his various valuable weapons and that he was  prepared to give either his body or his weapons.

Drona prayed to give him all his weapons together with the mysteries of hurling and recalling them and Rama gave all his weapons to Drona,

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If we study these 2 stories in depth, we will find 2 contradictions.

1)          If  the Parasu Rama the son of Jamadagni extirpated Kshatriya-s many times by going around the earth, then lineage of both Ikshvaku's, to which Dasaratha belonged, and Nimi's, to which Janaka belonged to, must have been broken, as Parasu Rama might have eliminated Kshatriya-s  of both lineages.

However, while describing the lineages of  Ikshvaku's and Nimi's during the marriage ceremony of Sri Rama and Sita, Sage Valmiki did not mention about breakage of those lineages due to Parasu Rama's adventures.

2)     In  Mahabharata it was mentioned that Drona obtained all his divine weapons from Parasu Rama.

Mahabharata followed Srimad Ramayana, as mention about Sri Rama can be found in Mahabharata but not about Pandavas in Srimad Ramayana.  Many such instances can be quoted.

So if Parasu Rama distributed all his riches along with entire land on earth to Kashyapa and retired to Mt. Mahendra for practising ascesis,  how can he still wait for Drona of Mahabharata era for  imparting knowledge in divine weapons and then retire to Mt. Mahendra?

The answer is clear.   

Parasu Rama existed only in Mahabharata era but not in Srimad Ramayana era.  Some learned Vaishnavites might have inserted at a latter date the story of Parasu Rama confronting Sri Rama, the son of Dasaratha, in Srimad Ramayana to make believe the readers that Rama the son of Jamadagni was holder  of  Supreme Vaishnava Bow and he was infact  the incarnation of Lord Vishnu.

Hence, we can conclude that Parasu Rama was not the incarnation of Lord Vishnu.