The fact that anything loses it's life is a result of sin.
If a spider is a threat to a human or beloved pet, the death of the spider would be a lesser evil than the death of a person or pet.
Yet, if one went berserk with pesticides, potentially poisoning everything and everyone in an effort to "kill spiders", then that would be quite an error in judgment.
Spiders outside the house keep other pesky and potentially deadly/damaging insects in check.
Some types of fear are largely based upon ignorance. Studying about spiders, their routines/roles in nature, and learning to identify the dangerous ones from the relatively harmless ones, should help allay any overblown/unreasonable fears regarding them.
Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempts he any man:
But every man is tempted, when he is drawn away of his own lust, and enticed.
Then when lust hath conceived, it brings forth sin: and sin, when it is finished, brings forth death. <-----> James 1:13-15
And I heard a great voice out of heaven saying, Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God.
And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away. <-----> Revelation 21:3+4
May God Be Glorified !
wm