The context will be clearer by reading from Matt 10:32-39, and by reading the parallel passage in Luke 12:8-12:
Mat 10:32 Everyone therefore who confesses me before men, him I will also confess before my Father who is in heaven.
Mat 10:33 But whoever denies me before men, him I will also deny before my Father who is in heaven.
Mat 10:34 "Don't think that I came to send peace on the earth. I didn't come to send peace, but a sword.
Mat 10:35 For I came to set a man at odds against his father, and a daughter against her mother, and a daughter-in-law against her mother-in-law.
Mat 10:36 A man's foes will be those of his own household.
Mat 10:37 He who loves father or mother more than me is not worthy of me; and he who loves son or daughter more than me isn't worthy of me.
Mat 10:38 He who doesn't take his cross and follow after me, isn't worthy of me.
Mat 10:39 He who seeks his life will lose it; and he who loses his life for my sake will find it.
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Luk 12:8 "I tell you, everyone who confesses me before men, him will the Son of Man also confess before the angels of God;
Luk 12:9 but he who denies me in the presence of men will be denied in the presence of the angels of God.
Luk 12:10 Everyone who speaks a word against the Son of Man will be forgiven, but those who blaspheme against the Holy Spirit will not be forgiven.
Luk 12:11 When they bring you before the synagogues, the rulers, and the authorities, don't be anxious how or what you will answer, or what you will say;
Luk 12:12 for the Holy Spirit will teach you in that same hour what you must say."
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I think we may look at it in the following perspective:
1. Profound fear and reverence towards Christ.
2. Trust and obedience.
3. Persevering and remaining faithful amid sufferings, persecutions, even unto death. Very dreadful situations that we may inevitably pass where what we may only do is to pray pervently, begging God that we may remain faithful.
4. Admonition to love God above all things, inwardly and outwardly.
5. A word of comfort that He is with us unto the end.
6. Etc, etc.
As to the question related to 'eternal damnation' we may compare J. Escariot and Peter and learn from there.
As to its implication related to 'witnessing & evangelism' is another aspect to be discussed.