Both Masses have the same essential parts - the Liturgy of the Word and the Liturgy of the Eucharist.
Those who say that it “Just came up”, or try to say that it was due to Protestants, or modeled on Protestant services are in largest part simply ignorant of the last 100 years of liturgical research.
At least in part, the attempt in shaping the new rubrics and revising the prayers was to return to the early Church.
To those who say that it was not an organic development based on changes to the Mass as we had it prior to Vatican 2, one can only agree, as it went beyond a few simple changes, or even a few not so simple changes.
Whether it was wise or not, there were significant changes to the Mass in both rubrics and prayers. There were those who felt that the rubrics of the Extraordinary Form had become almost problematic, in that they reflected almost exclusively the transcendence of God; in the changes there was an attempt to balance transcendence with immanence, and the Sacrificial aspect with the Mass with the Sacred Meal aspect (“take and eat; take and drink”). Some feel that it went too far in the other direction; some will even say that it eliminated sacrifice and transcendence. That it impacted both issues is undeniable; whether or not it went too far is perhaps another issue. However, there will be little or no convincing those who do not like the Ordinary Form that it did not.
Anyone who says that the Mass in the OF is not a true Mass is someone who is abysmally ignorant of what makes up the Mass, and what the differences are between the two forms. They are best just left alone as they would appear to exhibit the same mindset of extreme liberals: “Don’t confuse me with the facts, as I already have my mind made up!” They focus on what they perceive to be the essentials of the Mass and essentials of the Consecration; they ignore what the Magisterium of the Church teaches about the Mass; they border of conspiratorialists, a group notoriously disconnected with reality, and they are abysmally ignorant not only of the Latin rite theology, but the accepted theology of the Church as a whole, which includes the Eastern rites (as a point, try to define when the Eucharist is actually confected, as it varies between Eastern rite theology and Western rite theology).
Attempting to enter into a discussion with someone who “knows” that you are wrong is an exercise in futility. Arguing with them is dangerous: never argue with a fool, as an observer may not be able to tell who is who.
There is nothing wrong at all in liking one form over the other, or preferring one form over the other. But saying that the OF is not a true Mass is to deny the teaching of the Magisterium of the Church, a place where only fools and heretics go. Best not to get involved.
Thanks.